Year 6 Maths: Highest Common Factors

Introduction to Highest Common Factors (HCF)

Hello Year 6! Today, we’re going to explore a concept called the Highest Common Factor, often shortened to HCF. This is a really useful idea in maths, especially when we want to simplify fractions or solve problems involving groups.

What is the Highest Common Factor?

The Highest Common Factor of two or more numbers is the biggest number that can divide all of them without leaving a remainder. In simpler terms, it’s the largest number that the numbers you are looking at can share as a factor.

How to Find the HCF

There are two main methods to find the HCF of numbers:

1. Listing the Factors:
   • A factor is a number that divides another number exactly, without leaving a remainder.
   • To find the HCF, you can list the factors of each number and then find the largest one they have in common.
   Example:
   • Let’s find the HCF of 12 and 16.
     • Factors of 12: 1, 2, 3, 4, 6, 12
     • Factors of 16: 1, 2, 4, 8, 16
     • Common factors: 1, 2, 4
     • The highest common factor is 4.
2. Using Prime Factorisation:
   • This method involves breaking the numbers down into their prime factors and then multiplying the smallest powers of the common prime factors.
   Example:
   • Find the HCF of 24 and 36.
     • Prime factors of 24: ( 2^3 \times 3^1 )
     • Prime factors of 36: ( 2^2 \times 3^2 )
     • The common prime factors are ( 2 ) and ( 3 ).
     • The lowest powers are ( 2^2 ) and ( 3^1 ).
     • Multiply them: ( 2^2 \times 3^1 = 4 \times 3 = 12 ).
     • So, the HCF is 12.

Key Rules for Finding the HCF

• The HCF is always less than or equal to the smallest number you are looking at.
• If the numbers are the same, the HCF is that number.
• If the numbers share no common factors other than 1, then the HCF is 1.

Tips and Tricks

• Use a Factor Tree: A factor tree can help you break down numbers into their prime factors easily.
• Practice with Pairs: Start by practicing with pairs of small numbers to build your confidence.
• Check Your Work: After finding the HCF, you can check it by dividing all the original numbers by the HCF to see if there’s no remainder.

Questions on Highest Common Factors

Easy Level Questions

1. What is the HCF of 6 and 9?
2. Find the HCF of 8 and 12.
3. What is the HCF of 5 and 10?
4. Find the HCF of 15 and 25.
5. What is the HCF of 10 and 20?
6. Find the HCF of 18 and 24.
7. What is the HCF of 14 and 28?
8. Find the HCF of 4 and 16.
9. What is the HCF of 12 and 18?
10. Find the HCF of 9 and 27.
11. What is the HCF of 2 and 8?
12. Find the HCF of 30 and 45.
13. What is the HCF of 3 and 12?
14. Find the HCF of 16 and 32.
15. What is the HCF of 24 and 36?
16. Find the HCF of 8 and 24.
17. What is the HCF of 20 and 25?
18. Find the HCF of 6 and 18.
19. What is the HCF of 9 and 9?
20. Find the HCF of 10 and 100.

Medium Level Questions

1. What is the HCF of 12 and 30?
2. Find the HCF of 45 and 75.
3. What is the HCF of 16 and 40?
4. Find the HCF of 36 and 60.
5. What is the HCF of 27 and 81?
6. Find the HCF of 14 and 49.
7. What is the HCF of 20 and 35?
8. Find the HCF of 24 and 60.
9. What is the HCF of 28 and 56?
10. Find the HCF of 18 and 54.
11. What is the HCF of 15 and 45?
12. Find the HCF of 32 and 48.
13. What is the HCF of 10, 20, and 30?
14. Find the HCF of 36, 48, and 60.
15. What is the HCF of 12, 18, and 24?
16. Find the HCF of 42 and 56.
17. What is the HCF of 25 and 50?
18. Find the HCF of 30, 45, and 75.
19. What is the HCF of 14, 28, and 42?
20. Find the HCF of 45 and 90.

Hard Level Questions

1. What is the HCF of 72 and 120?
2. Find the HCF of 84 and 126.
3. What is the HCF of 54 and 81?
4. Find the HCF of 48 and 180.
5. What is the HCF of 64 and 96?
6. Find the HCF of 56 and 84.
7. What is the HCF of 60 and 150?
8. Find the HCF of 200 and 300.
9. What is the HCF of 77 and 154?
10. Find the HCF of 90 and 270.
11. What is the HCF of 63 and 126?
12. Find the HCF of 36, 60, and 72.
13. What is the HCF of 40 and 100?
14. Find the HCF of 50, 100, and 150.
15. What is the HCF of 32 and 128?
16. Find the HCF of 96 and 144.
17. What is the HCF of 18, 30, and 42?
18. Find the HCF of 72, 48, and 36.
19. What is the HCF of 144 and 216?
20. Find the HCF of 90, 120, and 150.

Answers and Explanations

Easy Level Answers

1. 3
2. 4
3. 5
4. 5
5. 10
6. 6
7. 14
8. 4
9. 6
10. 9
11. 2
12. 15
13. 3
14. 16
15. 12
16. 8
17. 5
18. 6
19. 9
20. 10

Medium Level Answers

1. 6
2. 15
3. 8
4. 12
5. 9
6. 7
7. 5
8. 12
9. 28
10. 18
11. 15
12. 16
13. 10
14. 12
15. 6
16. 14
17. 25
18. 15
19. 14
20. 15

Hard Level Answers

1. 24
2. 42
3. 27
4. 12
5. 32
6. 28
7. 30
8. 100
9. 77
10. 90
11. 63
12. 12
13. 20
14. 50
15. 32
16. 48
17. 6
18. 36
19. 72
20. 30

Now you have a good understanding of the Highest Common Factor! Keep practising, and you’ll become a pro in no time!