Year 6 Maths: Finding Factors by Dividing

Introduction to Factors

Hello, Year 6! Today, we’re going to learn about factors and how to find them using division. A factor is a number that can be multiplied by another number to make a product. For example, in the multiplication 2 × 3 = 6, both 2 and 3 are factors of 6.

What Are Factors?

Factors of a number are all the whole numbers that can divide that number without leaving a remainder.

Example:

• Factors of 12:
  • 1 (because 1 × 12 = 12)
  • 2 (because 2 × 6 = 12)
  • 3 (because 3 × 4 = 12)
  • 4, 6, and 12 are also factors.

So, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Finding Factors by Dividing

To find the factors of a number using division, we can divide the number by smaller numbers to see if they divide evenly.

Steps to Find Factors:

1. Start with the number 1 and divide the target number by it. If there’s no remainder, it’s a factor!
2. Continue dividing by whole numbers (2, 3, 4, etc.) until you reach the number itself.
3. If the division does not leave a remainder, then the number you divided by is a factor.

Key Rules:

• Dividing by 1 and the number itself: Every number has at least two factors, which are 1 and the number itself.
• Only whole numbers: We only look for whole number factors.

Example: Finding Factors of 18

1. Divide by 1:
   • $$18 ÷ 1 = 18$$ (no remainder, so 1 is a factor)
2. Divide by 2:
   • $$18 ÷ 2 = 9$$ (no remainder, so 2 is a factor)
3. Divide by 3:
   • $$18 ÷ 3 = 6$$ (no remainder, so 3 is a factor)
4. Divide by 4:
   • $$18 ÷ 4 = 4.5$$ (this has a remainder, so 4 is not a factor)
5. Continue until you reach 18.

The factors of 18 are 1, 2, 3, 6, 9, and 18.

Tips and Tricks

• Use a calculator if you’re unsure about your division!
• Make a list: Write down the numbers you’re testing to keep track.
• Remember: If you find a factor (like 2), you can also find its pair (like 9 for 18) by dividing the number by that factor.

Practice Questions

Easy Level

1. What are the factors of 6?
2. Find the factors of 8.
3. List the factors of 10.
4. What factors can you find for 4?
5. Identify the factors of 9.
6. What are the factors of 15?
7. List the factors of 14.
8. Find the factors of 16.
9. What are the factors of 20?
10. List the factors for 12.

Medium Level

11. Identify the factors of 24.
12. What are the factors of 30?
13. List the factors of 36.
14. Find the factors of 28.
15. What factors can you find for 32?
16. Identify the factors of 40.
17. What are the factors of 45?
18. List the factors of 50.
19. Find the factors of 60.
20. What factors can you find for 72?

Hard Level

21. Find the factors of 84.
22. What are the factors of 100?
23. Identify the factors of 120.
24. List the factors for 144.
25. What factors can you find for 150?
26. Identify the factors of 180.
27. What are the factors of 200?
28. List the factors of 225.
29. Find the factors of 256.
30. What factors can you find for 300?

Answers and Explanations

Easy Level Answers

1. 1, 2, 3, 6
2. 1, 2, 4, 8
3. 1, 2, 5, 10
4. 1, 2, 4
5. 1, 3, 9
6. 1, 3, 5, 15
7. 1, 2, 7, 14
8. 1, 2, 4, 8, 16
9. 1, 2, 4, 5, 10, 20
10. 1, 2, 3, 4, 6, 12

Medium Level Answers

11. 1, 2, 3, 4, 6, 8, 12, 24
12. 1, 2, 3, 5, 6, 10, 15, 30
13. 1, 2, 3, 4, 6, 9, 12, 18, 36
14. 1, 2, 4, 7, 14, 28
15. 1, 2, 4, 8, 16, 32
16. 1, 2, 4, 5, 8, 10, 20, 40
17. 1, 3, 5, 9, 15, 45
18. 1, 2, 5, 10, 25, 50
19. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
20. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Hard Level Answers

21. 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
22. 1, 2, 4, 5, 10, 20, 25, 50, 100
23. 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 60, 120
24. 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
25. 1, 2, 3, 5, 6, 10, 15, 30, 50, 75, 150
26. 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 60, 90, 180
27. 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
28. 1, 3, 5, 9, 15, 25, 45, 75, 225
29. 1, 2, 4, 8, 16, 32, 64, 256
30. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 60, 75, 100, 150, 300

Conclusion

Now you know how to find factors using division! Keep practicing, and soon it will become very easy. Happy dividing!