🚀🚀Common Factors and Highest Common Factors🚀🚀

 Welcome 👦👧boys and girls to another class. Today, we will be going on an adventure where we will be exploring some Common Factors and Highest Common Factors. Read all information carefully before writing your answers. Show all working.


What is a Factor?
A factor is a number that divides exactly into another number (with no leftovers).

  • Example: The factors of 12 are: 1, 2, 3, 4, 6, and 12. (Because 12 ÷ 3 = 4 exactly).
2.The Definition Common Factor: A number that is a factor of two or more numbers.
    • Example: The factors of 12 are (1, 2, 3, 4, 6, 12) and the factors of 18 are (1, 2, 3, 6, 9, 18). The common factors are 1, 2, 3, and 6.
  • Greatest Common Factor (GCF): The largest number on the list of common factors.
    • Example: For 12 and 18, the common factors are 1, 2, 3, and 6. The Greatest Common Factor is 6.

  • Examples (Step-by-Step)

    Example 1: Find the common factors of 8 and 12.

    • Step 1: List all factors of 8. (1, 2, 4, 8)
    • Step 2: List all factors of 12. (1, 2, 3, 4, 6, 12)
    • Step 3: Circle the numbers that appear in both lists. (1, 2, 4)
    • Answer: The common factors are 1, 2, and 4.

    Example 2: Find the Greatest Common Factor (GCF) of 15 and 20.

    • Step 1: Factors of 15: (1, 3, 5, 15)
    • Step 2: Factors of 20: (1, 2, 4, 5, 10, 20)
    • Step 3: Common factors: (1, 5)
    • Step 4: The biggest number in the common list is 5.
    • Answer: The GCF is 5.

3. What is the Highest Common Factor (H.C.F.)?
This is the biggest number that appears on the factor lists of two different numbers at the same time. It is the largest number that can divide both of them exactly.

  • The "Easy" Trick: Write down all the factors of both numbers, circle the ones they share, and pick the biggest one! 

4. What is the Highest Factor (or Greatest Factor)?
This is simply the biggest number on that list of factors. For any number, the highest factor is always the number itself.

  • Example: The highest factor of 12 is 12.
  • Example: The highest factor of 25 is 25.

Part 2: Examples (Step-by-Step)

Example 1: Find the Highest Common Factor (H.C.F.) of 8 and 12.

  • Step 1: List factors of 8 → 1, 2, 4, 8
  • Step 2: List factors of 12 → 1, 2, 3, 4, 6, 12
  • Step 3: Find the common ones (they both have) → 1, 2, 4
  • Step 4: Pick the biggest one → 4.
  • Answer: The H.C.F. of 8 and 12 is 4.

Example 2: Find the Highest Common Factor (H.C.F.) of 15 and 20.

  • Step 1: List factors of 15 → 1, 3, 5, 15
  • Step 2: List factors of 20 → 1, 2, 4, 5, 10, 20
  • Step 3: Find the common ones → 1, 5
  • Step 4: Pick the biggest one → 5.
  • Answer: The H.C.F. of 15 and 20 is 5. 
Task1:

 Circle the correct answer.

  1. What are the factors of 6?
    • a) 1, 2, 3, 6
    • b) 1, 2, 4, 6
    • c) 2, 3, 4
  2. What is the highest factor of 14?
    • a) 7
    • b) 14
    • c) 1
  3. What is the H.C.F. of 4 and 6?
    • a) 4
    • b) 6
    • c) 2
  4. What is the H.C.F. of 10 and 15?
    • a) 5
    • b) 10
    • c) 15
  5. What are the factors of 18?
    • a) 1, 2, 3, 6, 9, 18
    • b) 1, 2, 4, 6, 9, 18
    • c) 1, 3, 5, 9, 18
  6. What is the highest factor of 25?
    • a) 5
    • b) 25
    • c) 1
  7. What is the H.C.F. of 9 and 12?
    • a) 9
    • b) 3
    • c) 1
  8. What is the H.C.F. of 14 and 21?
    • a) 14
    • b) 21
    • c) 7
  9. Which number is a factor of both 16 and 24?
    • a) 5
    • b) 8
    • c) 10
  10. What is the H.C.F. of 5 and 7?
    • a) 35
    • b) 5
    • c) 1 

  11. What are the common factors of 6 and 10?

    • A) 1, 2
    • B) 1, 2, 3
    • C) 1, 2, 5
    • D) 1, 2, 6

    12. What is the Greatest Common Factor (GCF) of 14 and 21?

    • A) 1
    • B) 3
    • C) 7
    • D) 14

    13. Which number is a common factor of 9, 18, and 27?

    • A) 4
    • B) 6
    • C) 9
    • D) 27

    14. What is the GCF of 24 and 36?

    • A) 6
    • B) 12
    • C) 18
    • D) 24 

Task2:

Write "True" or "False" next to each number.

  1. The factors of 10 are 1, 2, 5, and 10. _______
  2. The highest factor of 20 is 10. _______
  3. The H.C.F. of 6 and 9 is 3. _______
  4. The number 4 is a factor of 15. _______
  5. The H.C.F. of 8 and 16 is 8. _______
  6. The highest factor of any number is always 1. _______
  7. The H.C.F. of 12 and 18 is 6. _______
  8. The number 7 is a factor of 21. _______
  9. The H.C.F. of 2 and 4 is 2. _______
  10. If two numbers are both odd, their H.C.F. can never be 1. _______ 

  11. The number 1 is a common factor of every pair of numbers.

    • Answer: _______

    12. The common factors of 10 and 15 are 1 and 5 only.

    • Answer: _______

    13. The GCF of 8 and 12 is 4.

    • Answer: _______

    14. If two numbers are 5 and 7, their only common factor is 1.

    • Answer: _______

     Task 3:

Write the correct answer in the blank space.

  1. The factors of 16 are 1, 2, 4, 8, and ______.
  2. The highest factor of 30 is ______.
  3. The common factors of 6 and 8 are 1 and ______.
  4. The H.C.F. of 6 and 8 is ______.
  5. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and ______.
  6. The H.C.F. of 10 and 20 is ______.
  7. The number 3 is a factor of both 9 and ______ (choose: 10 or 15).
  8. The H.C.F. of 16 and 20 is ______.
  9. The highest factor of 45 is ______.
  10. The H.C.F. of 3 and 9 is ______.

Task 4: Liveworksheets 

Click and do  the 


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