Prime Numbers Odd Numbers Even Numbers Lowest Common Multiple Highest Common Factor Mathematics Primary 5 First Term Lesson Notes Week 5

Title: Identification of Prime and Composite Numbers, LCM, and HCF

Subject: Mathematics

Class: Primary 5

Term: First Term

Week: 5

Topic: Prime Numbers, LCM, and HCF

Duration: 45 minutes

Learning Objectives:

1. To identify odd and even numbers.
2. To recognize prime numbers less than 200.
3. To understand the concept of Lowest Common Multiple (LCM).
4. To comprehend the concept of Highest Common Factor (HCF).

Previous Lesson: Multiplication and Division of Whole Numbers

Embedded Core Skills:

• Numeracy
• Problem-solving
• Critical thinking

Learning Materials:

• Chalkboard/whiteboard
• Chalk/markers
• Slides or flashcards with numbers
• Chart with prime numbers less than 200
• Worksheets with exercises

Content:

1. Introduction to Odd and Even Numbers : Odd numbers are numbers that can be divided by two with one as the remainder eg 1,3,5,7,9,etc while even numbers are the numbers that can be divided by two with zero as the remainder eg 0,2,4,6,8,etc
   • Explain the difference between odd and even numbers.
   • Give examples and ask students to identify more.
2. Prime numbers are special numbers that have only two factors: 1 and themselves. In other words, prime numbers can only be divided by 1 and the number itself, without leaving a remainder.Here are some examples of prime numbers:
   1. 2: The number 2 is the smallest prime number because it can only be divided by 1 and 2.
   2. 3: 3 is also a prime number because it can only be divided by 1 and 3.
   3. 5: 5 is another prime number because it has only two factors, 1 and 5.
   4. 7: 7 is a prime number as well because it can be divided only by 1 and 7.
   5. 11: 11 is a prime number since it has no other factors except for 1 and 11.

   Now, let’s look at a non-prime number as an example:

   6. 6: 6 is not a prime number because it can be divided by 1, 2, 3, and 6. It has more than two factors.

   To find prime numbers, you can start with small numbers and check if they have only two factors, 1 and themselves. If they do, they are prime! It’s like a special club where only a few numbers are allowed to join. Prime numbers are essential in mathematics and have many applications in various fields

3. What are prime factors? 
   1. Prime factors are the prime numbers that, when multiplied together, give you a particular composite number. In other words, they are the building blocks of a composite number.Here’s how to find the prime factors of a number:
      1. Start with the number you want to factor.
      2. Divide the number by the smallest prime number (2) and continue dividing until you can’t divide anymore.
      3. Write down each prime factor as you go.
      4. Move on to the next prime number and repeat the process until the original number becomes 1.

      For example, let’s find the prime factors of 12:

      1. Start with 12.
      2. 12 ÷ 2 = 6 (2 is a prime factor, so write it down).
      3. 6 ÷ 2 = 3 (2 is a prime factor, and 3 is also a prime number, so write both down).

      So, the prime factors of 12 are 2 and 3.

      Here’s another example with a larger number, 28:

      1. Start with 28.
      2. 28 ÷ 2 = 14 (2 is a prime factor, so write it down).
      3. 14 ÷ 2 = 7 (2 is a prime factor, and 7 is also a prime number, so write both down).

      So, the prime factors of 28 are 2 and 7.

      Finding the prime factors of a number is important in various mathematical calculations, including simplifying fractions, finding common factors, and solving equations

How to Calculate prime numbers of given figures 

1. • Number: 12
     • Start with 12.
     • Divide by the smallest prime, 2: 12 ÷ 2 = 6.
     • Divide 6 by 2 again: 6 ÷ 2 = 3.
     • Write down the prime factors: 2 and 3.
     • So, the prime factors of 12 are 2 and 3.
   • Number: 20
     • Start with 20.
     • Divide by 2: 20 ÷ 2 = 10.
     • Divide 10 by 2 again: 10 ÷ 2 = 5.
     • Write down the prime factors: 2 and 5.
     • So, the prime factors of 20 are 2 and 5.
   • Number: 48
     • Start with 48.
     • Divide by 2: 48 ÷ 2 = 24.
     • Divide 24 by 2 again: 24 ÷ 2 = 12.
     • Divide 12 by 2 again: 12 ÷ 2 = 6.
     • Divide 6 by 2 again: 6 ÷ 2 = 3.
     • Write down the prime factors: 2 and 3.
     • So, the prime factors of 48 are 2 and 3.
   • Number: 15
     • Start with 15.
     • Divide by 3: 15 ÷ 3 = 5.
     • Write down the prime factors: 3 and 5.
     • So, the prime factors of 15 are 3 and 5.
   • Number: 56
     • Start with 56.
     • Divide by 2: 56 ÷ 2 = 28.
     • Divide 28 by 2 again: 28 ÷ 2 = 14.
     • Divide 14 by 2 again: 14 ÷ 2 = 7.
     • Write down the prime factors: 2 and 7.
     • So, the prime factors of 56 are 2 and 7.
   • Number: 100
     • Start with 100.
     • Divide by 2: 100 ÷ 2 = 50.
     • Divide 50 by 2 again: 50 ÷ 2 = 25.
     • Divide 25 by 5: 25 ÷ 5 = 5.
     • Write down the prime factors: 2 and 5.
     • So, the prime factors of 100 are 2 and 5.
   • Number: 21
     • Start with 21.
     • Divide by 3: 21 ÷ 3 = 7.
     • Write down the prime factor: 3 and 7.
     • So, the prime factors of 21 are 3 and 7.
   • Number: 36
     • Start with 36.
     • Divide by 2: 36 ÷ 2 = 18.
     • Divide 18 by 2 again: 18 ÷ 2 = 9.
     • Divide 9 by 3: 9 ÷ 3 = 3.
     • Write down the prime factors: 2 and 3.
     • So, the prime factors of 36 are 2 and 3.
   • Number: 63
     • Start with 63.
     • Divide by 3: 63 ÷ 3 = 21.
     • Divide 21 by 3 again: 21 ÷ 3 = 7.
     • Write down the prime factors: 3 and 7.
     • So, the prime factors of 63 are 3 and 7.
   • Number: 72
     • Start with 72.
     • Divide by 2: 72 ÷ 2 = 36.
     • Divide 36 by 2 again: 36 ÷ 2 = 18.
     • Divide 18 by 2 again: 18 ÷ 2 = 9.
     • Divide 9 by 3: 9 ÷ 3 = 3.
     • Write down the prime factors: 2 and 3.
     • So, the prime factors of 72 are 2 and 3.

2. Odd and even numbers are two categories of whole numbers:

   1. Even Numbers:
      • Even numbers are whole numbers that can be exactly divided by 2 without leaving a remainder.
      • Examples of even numbers: 2, 4, 6, 8, 10, and so on.
      • Notice that all even numbers end in 0, 2, 4, 6, or 8.
   2. Odd Numbers:
      • Odd numbers are whole numbers that cannot be divided by 2 evenly and always leave a remainder of 1 when divided by 2.
      • Examples of odd numbers: 1, 3, 5, 7, 9, and so on.
      • Odd numbers always end in 1, 3, 5, 7, or 9.

   In summary, even numbers are divisible by 2, while odd numbers are not divisible by 2. You can easily identify whether a number is even or odd by looking at its units digit (the digit on the right). If it’s even, it’s an even number; if it’s odd, it’s an odd number.

    
   Evaluation
   • An even number is always ______ by 2. a) Divisible b) Subtracted c) Multiplied d) Added
   • Odd numbers leave a remainder of ____ when divided by 2. a) 0 b) 1 c) 2 d) 3
   • The last digit of even numbers is usually ____. a) 1 b) 2 c) 4 d) 6
   • Which of these is an even number? a) 5 b) 7 c) 12 d) 15
   • All even numbers are multiples of ____. a) 2 b) 3 c) 5 d) 10
   • Odd numbers often end in ____. a) 0 b) 2 c) 4 d) 7
   • The sum of two even numbers is always ____. a) Even b) Odd c) Prime d) Fraction
   • What is the next odd number after 13? a) 14 b) 15 c) 16 d) 17
   • An even number plus an odd number equals an ____ number. a) Odd b) Even c) Prime d) Fraction
   • If you add two even numbers, the result is always ____. a) Even b) Odd c) Prime d) Zero
   • Which of these is an odd number? a) 8 b) 10 c) 13 d) 16
   • If you subtract an odd number from an even number, the result is ____. a) Even b) Odd c) Prime d) Zero
   • What is the double of an odd number? a) Even b) Odd c) Prime d) Fraction
   • If you multiply two odd numbers, the result is always ____. a) Even b) Odd c) Prime d) Zero
   • The product of an even number and any other number is always ____. a) Even b) Odd c) Prime d) Fraction
   • All Factors of Numbers
   • Factors of 12
     • Factors of 12 are numbers that can multiply to give 12.
     • Examples: 1 × 12 = 12, 2 × 6 = 12, 3 × 4 = 12.
     • So, the factors of 12 are 1, 2, 3, 4, 6, and 12.
   • Factors of 20
     • Factors of 20 are numbers that can multiply to give 20.
     • Examples: 1 × 20 = 20, 2 × 10 = 20, 4 × 5 = 20.
     • So, the factors of 20 are 1, 2, 4, 5, 10, and 20.
   • Factors of 36
     • Factors of 36 are numbers that can multiply to give 36.
     • Examples: 1 × 36 = 36, 2 × 18 = 36, 3 × 12 = 36, 4 × 9 = 36, 6 × 6 = 36.
     • So, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
   • Factors of 15
     • Factors of 15 are numbers that can multiply to give 15.
     • Examples: 1 × 15 = 15, 3 × 5 = 15.
     • So, the factors of 15 are 1, 3, 5, and 15.
   • Factors of 56
     • Factors of 56 are numbers that can multiply to give 56.
     • Examples: 1 × 56 = 56, 2 × 28 = 56, 4 × 14 = 56, 7 × 8 = 56.
     • So, the factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.
   • Factors of 21
     • Factors of 21 are numbers that can multiply to give 21.
     • Examples: 1 × 21 = 21, 3 × 7 = 21.
     • So, the factors of 21 are 1, 3, 7, and 21.
   • Factors of 63
     • Factors of 63 are numbers that can multiply to give 63.
     • Examples: 1 × 63 = 63, 3 × 21 = 63, 7 × 9 = 63.
     • So, the factors of 63 are 1, 3, 7, 9, 21, and 63.
   • Factors of 100
     • Factors of 100 are numbers that can multiply to give 100.
     • Examples: 1 × 100 = 100, 2 × 50 = 100, 4 × 25 = 100, 5 × 20 = 100, 10 × 10 = 100.
     • So, the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
   • Factors of 72
     • Factors of 72 are numbers that can multiply to give 72.
     • Examples: 1 × 72 = 72, 2 × 36 = 72, 3 × 24 = 72, 4 × 18 = 72, 6 × 12 = 72.
     • So, the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
   • • The factors of 12 are 1, ____, 3, 4, 6, and 12. a) 2 b) 5 c) 8 d) 9
     • A prime number has exactly ____ factors. a) 2 b) 3 c) 4 d) 5
     • The prime factors of 20 are 2 and ____. a) 4 b) 6 c) 8 d) 10
     • Factors of 24 are 1, 2, 3, 4, 6, 8, 12, and ____. a) 14 b) 15 c) 16 d) 24
     • A number with only two factors, 1 and itself, is called a ____ number. a) Composite b) Even c) Prime d) Odd
     • The prime factors of 15 are 3 and ____. a) 4 b) 5 c) 6 d) 7
     • The number 1 is a factor of ____ whole numbers. a) No b) Some c) All d) Odd
     • Factors of 28 are 1, 2, 4, 7, 14, and ____. a) 16 b) 21 c) 24 d) 28
     • To find prime factors, start with the smallest prime, which is ____. a) 1 b) 2 c) 3 d) 10
     • The only even prime number is ____. a) 1 b) 2 c) 3 d) 4
     • The factors of 10 are 1, 2, 5, and ____. a) 7 b) 10 c) 12 d) 15
     • A prime factorization is the expression of a number as a product of its ____ factors. a) Composite b) Prime c) Even d) Odd
     • The prime factors of 18 are 2 and ____. a) 4 b) 5 c) 6 d) 9
     • A number with more than two factors is called a ____ number. a) Prime b) Odd c) Even d) Composite
     • The prime factors of 56 are 2 and ____. a) 4 b) 7 c) 14 d) 28
3. Identification of Prime Numbers
   • Define prime numbers as numbers with exactly two factors: 1 and itself.
   • Introduce prime numbers less than 200.
   • Discuss and show prime numbers on the chart.
   • Prime Factors: Prime factors are the prime numbers that, when multiplied together, give you a specific number. They are the building blocks of a number.For example, let’s find the prime factors of 24:
     1. Start with 24.
     2. Divide by the smallest prime, which is 2: 24 ÷ 2 = 12.
     3. Divide 12 by 2 again: 12 ÷ 2 = 6.
     4. Divide 6 by 2 once more: 6 ÷ 2 = 3.
     5. Now, you have reached a prime number, 3. So, the prime factors of 24 are 2 and 3.

     All Factors (or Factors): All factors of a number are the whole numbers that can evenly divide that number without leaving a remainder. These factors can be prime or composite numbers.

     For example, let’s find all the factors of 12:

     1. Factors of 12 are numbers that can multiply to give 12.
     2. Examples: 1 × 12 = 12, 2 × 6 = 12, 3 × 4 = 12.
     3. So, the factors of 12 are 1, 2, 3, 4, 6, and 12.

     In summary:

     • Prime factors are the prime numbers that multiply to make a number.
     • All factors (or factors) are all the numbers that can divide a number evenly, including 1 and the number itself
4. Lowest Common Multiple (LCM)
   • Explain LCM as the smallest common multiple of two or more numbers.
   • Demonstrate finding LCM using examples on the board.
5. Highest Common Factor (HCF)
   • Explain HCF as the largest common factor/divisor of two or more numbers.
   • Show how to find HCF with examples.

1. Lowest Common Multiple (LCM):

The Lowest Common Multiple, or LCM, is the smallest multiple that two or more numbers share. In other words, it’s the smallest number that can be evenly divided by each of those numbers.

Example 1: Let’s find the LCM of 4 and 6.

• First, list the multiples of each number:
  • Multiples of 4: 4, 8, 12, 16, 20, …
  • Multiples of 6: 6, 12, 18, 24, 30, …
• The smallest number that appears in both lists is 12. So, the LCM of 4 and 6 is 12.

2. Highest Common Factor (HCF):

The Highest Common Factor, or HCF, is the largest number that can exactly divide two or more numbers without leaving a remainder. It’s also called the Greatest Common Divisor (GCD).

Example 2: Let’s find the HCF of 12 and 18.

• List the factors of each number:
  • Factors of 12: 1, 2, 3, 4, 6, 12
  • Factors of 18: 1, 2, 3, 6, 9, 18
• The largest number that appears in both lists is 6. So, the HCF of 12 and 18 is 6.

Summary:

• LCM is the smallest multiple shared by two or more numbers.
• HCF is the largest number that can divide two or more numbers without a remainder.
• You can find LCM by listing multiples, and you can find HCF by listing factors.
• LCM helps when you want to find a common multiple for different numbers, like in adding fractions.
• HCF helps when you want to simplify fractions or find common factors of numbers

Example 1: Finding LCM

Let’s find the LCM of 8 and 12.

• List the multiples of each number:
  • Multiples of 8: 8, 16, 24, 32, 40, …
  • Multiples of 12: 12, 24, 36, 48, 60, …
• The smallest number that appears in both lists is 24. So, the LCM of 8 and 12 is 24.

Example 2: Finding HCF

Let’s find the HCF of 18 and 24.

• List the factors of each number:
  • Factors of 18: 1, 2, 3, 6, 9, 18
  • Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
• The largest number that appears in both lists is 6. So, the HCF of 18 and 24 is 6.

Example 3: Finding LCM

Let’s find the LCM of 15 and 20.

• List the multiples of each number:
  • Multiples of 15: 15, 30, 45, 60, 75, …
  • Multiples of 20: 20, 40, 60, 80, 100, …
• The smallest number that appears in both lists is 60. So, the LCM of 15 and 20 is 60.

Example 4: Finding HCF

Let’s find the HCF of 36 and 48.

• List the factors of each number:
  • Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
  • Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
• The largest number that appears in both lists is 12. So, the HCF of 36 and 48 is 12

Example 5: Finding LCM

Let’s find the LCM of 9 and 15.

• List the multiples of each number:
  • Multiples of 9: 9, 18, 27, 36, 45, …
  • Multiples of 15: 15, 30, 45, 60, 75, …
• The smallest number that appears in both lists is 45. So, the LCM of 9 and 15 is 45.

Example 6: Finding HCF

Let’s find the HCF of 28 and 42.

• List the factors of each number:
  • Factors of 28: 1, 2, 4, 7, 14, 28
  • Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
• The largest number that appears in both lists is 14. So, the HCF of 28 and 42 is 14.

Example 7: Finding LCM

Let’s find the LCM of 6, 8, and 10.

• List the multiples of each number:
  • Multiples of 6: 6, 12, 18, 24, 30, …
  • Multiples of 8: 8, 16, 24, 32, 40, …
  • Multiples of 10: 10, 20, 30, 40, 50, …
• The smallest number that appears in all three lists is 24. So, the LCM of 6, 8, and 10 is 24.

Example 8: Finding HCF

Let’s find the HCF of 16, 24, and 32.

• List the factors of each number:
  • Factors of 16: 1, 2, 4, 8, 16
  • Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
  • Factors of 32: 1, 2, 4, 8, 16, 32
• The largest number that appears in all three lists is 8. So, the HCF of 16, 24, and 32 is 8.

Example 9: Finding LCM

Let’s find the LCM of 5 and 7.

• List the multiples of each number:
  • Multiples of 5: 5, 10, 15, 20, 25, …
  • Multiples of 7: 7, 14, 21, 28, 35, …
• The smallest number that appears in both lists is 35. So, the LCM of 5 and 7 is 35.

Example 10: Finding HCF

Let’s find the HCF of 20 and 25.

• List the factors of each number:
  • Factors of 20: 1, 2, 4, 5, 10, 20
  • Factors of 25: 1, 5, 25
• The largest number that appears in both lists is 5. So, the HCF of 20 and 25 is 5

1. The LCM is the ______ multiple shared by two or more numbers. a) Smallest b) Largest c) Oldest d) Fanciest
2. The HCF is the ______ number that can divide two or more numbers without a remainder. a) Smallest b) Tallest c) Coldest d) Newest
3. To find LCM, you list ______ of numbers. a) Multiples b) Dividends c) Addends d) Factors
4. To find HCF, you list ______ of numbers. a) Multiples b) Divisors c) Factors d) Decimals
5. The LCM helps in adding and subtracting ______ with different denominators. a) Numbers b) Fractions c) Letters d) Shapes
6. The HCF is useful for simplifying ______. a) Equations b) Decimals c) Fractions d) Words
7. Find the LCM of 4 and 6: LCM = ______ a) 10 b) 8 c) 12 d) 14
8. Find the HCF of 18 and 24: HCF = ______ a) 4 b) 6 c) 8 d) 10
9. LCM of 7 and 9 is: LCM = ______ a) 54 b) 63 c) 81 d) 45
10. HCF of 16 and 20 is: HCF = ______ a) 4 b) 5 c) 6 d) 8
11. Find the LCM of 3, 5, and 7: LCM = ______ a) 15 b) 21 c) 35 d) 42
12. HCF of 12 and 15 is: HCF = ______ a) 2 b) 3 c) 5 d) 4
13. LCM of 8 and 10 is: LCM = ______ a) 20 b) 25 c) 30 d) 35
14. HCF of 36 and 48 is: HCF = ______ a) 6 b) 8 c) 10 d) 12
15. Find the LCM of 2, 4, and 6: LCM = ______ a) 6 b) 8 c) 10 d) 12

Presentation: Step 1: Begin with a recap of the previous lesson on multiplication and division.

Step 2: Introduce the concept of odd and even numbers, engaging students in identifying examples.

Step 3: Teach about prime numbers, presenting the list of prime numbers less than 200.

Teacher’s Activities:

• Write key points and examples on the board.
• Use visual aids to facilitate understanding.
• Encourage student participation and questions.

Learners’ Activities:

• Listen actively and take notes.
• Participate in discussions.
• Solve problems on the board.

Assessment:

• Use worksheets with exercises on identifying prime numbers, LCM, and HCF.
• Ask students to find the LCM and HCF of specific numbers.
• Evaluate their understanding during class activities.

Evaluation Questions:

1. Is 17 an odd or even number?
2. List the prime numbers less than 200.
3. Calculate the LCM of 4 and 6.
4. What is the HCF of 12 and 18?

Conclusion:

• Summarize the key points of the lesson.
• Reinforce the importance of understanding odd/even numbers, prime numbers, LCM, and HCF.
• Assign homework for further practice