Year 6 Maths: Prime Factors

What are Prime Factors?

Hello Year 6! Today, we’re going to learn about prime factors. Understanding prime factors is an important part of maths, and it can help you with many problems.

What is a Factor?

First, let’s remember what a factor is. A factor is a number that can divide another number without leaving a remainder. For example, the factors of 10 are 1, 2, 5, and 10 because:

• 10 ÷ 1 = 10
• 10 ÷ 2 = 5
• 10 ÷ 5 = 2
• 10 ÷ 10 = 1

What is a Prime Number?

Next, we need to know about prime numbers. A prime number is a special kind of number that can only be divided by 1 and itself. This means it has exactly two factors. For example:

• 2 is prime because its only factors are 1 and 2.
• 3 is prime because its only factors are 1 and 3.
• 4 is not prime because it can be divided by 1, 2, and 4.

What are Prime Factors?

Now, let’s put it all together. Prime factors are the prime numbers that multiply together to make a certain number. In other words, they are the prime numbers that are factors of that number.

Example:

Let’s find the prime factors of 12:

1. First, we find all the factors of 12: 1, 2, 3, 4, 6, 12.
2. Now, we identify which of these are prime: 2 and 3.
3. Therefore, the prime factors of 12 are 2 and 3.

We can also write this as:

$$12 = 2 \times 2 \times 3$$

or

$$12 = 2^2 \times 3$$

Key Rules to Remember

1. Prime numbers have only two factors: 1 and themselves.
2. Any whole number greater than 1 can be broken down into prime factors.
3. The same prime factor can be used more than once.

Tips and Tricks

• Start by dividing the number by the smallest prime number (2) and keep going until you can’t divide anymore.
• Make a list of the prime factors as you go along.
• If you’re unsure if a number is prime, check if it can be divided by any prime numbers less than its square root.

Questions for Practice

Easy Level Questions (1-20)

1. What are the prime factors of 10?
2. Is 5 a prime number?
3. What is a factor of 6?
4. List the factors of 8.
5. What are the prime factors of 15?
6. Is 7 a prime number?
7. What are the factors of 12?
8. List the prime factors of 18.
9. Is 9 a prime number?
10. What are the factors of 20?
11. What is the smallest prime number?
12. What are the prime factors of 21?
13. List the factors of 16.
14. What is a factor of 14?
15. Is 11 a prime number?
16. What are the prime factors of 22?
17. What are the factors of 24?
18. List the prime factors of 30.
19. Is 10 a prime number?
20. What is the largest prime number less than 20?

Medium Level Questions (21-40)

21. What are the prime factors of 36?
22. Is 25 a prime number?
23. What are the factors of 28?
24. List the prime factors of 32.
25. What is the product of the prime factors of 14?
26. What are the prime factors of 45?
27. Is 18 a prime number?
28. What are the factors of 42?
29. List the prime factors of 50.
30. What is the smallest prime number greater than 10?
31. What are the prime factors of 60?
32. Is 27 a prime number?
33. What are the factors of 48?
34. List the prime factors of 70.
35. What is the product of the prime factors of 36?
36. What are the prime factors of 81?
37. Is 16 a prime number?
38. What are the factors of 90?
39. List the prime factors of 100.
40. What is the largest prime number less than 30?

Hard Level Questions (41-60)

41. What are the prime factors of 72?
42. Is 49 a prime number?
43. What are the factors of 84?
44. List the prime factors of 96.
45. What is the product of the prime factors of 48?
46. What are the prime factors of 120?
47. Is 64 a prime number?
48. What are the factors of 108?
49. List the prime factors of 150.
50. What is the smallest prime number greater than 20?
51. What are the prime factors of 135?
52. Is 33 a prime number?
53. What are the factors of 144?
54. List the prime factors of 180.
55. What is the product of the prime factors of 72?
56. What are the prime factors of 200?
57. Is 50 a prime number?
58. What are the factors of 240?
59. List the prime factors of 300.
60. What is the largest prime number less than 50?

Answers and Explanations

Easy Level Answers

1. 2, 5
2. Yes
3. 1, 2, 3, 6
4. 1, 2, 4, 8
5. 3, 5
6. Yes
7. 1, 2, 3, 4, 6, 12
8. 2, 3
9. No
10. 1, 2, 4, 5, 10, 20
11. 2
12. 3, 7
13. 1, 2, 4, 8, 16
14. 1, 2, 7, 14
15. Yes
16. 2, 11
17. 1, 2, 3, 4, 6, 8, 12, 24
18. 2, 3, 5
19. No
20. 19

Medium Level Answers

21. 2, 3
22. No
23. 1, 2, 4, 7, 14, 28
24. 2, 2, 2, 2
25. 2 × 7 = 14
26. 3, 5
27. No
28. 1, 2, 3, 6, 7, 14, 21, 42
29. 2, 5
30. 11
31. 2, 3, 5
32. No
33. 1, 2, 3, 4, 6, 8, 9, 12, 16, 24, 36, 48
34. 2, 5, 7
35. 2 × 3 × 2 = 36
36. 3
37. No
38. 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 72, 108
39. 2, 5
40. 29

Hard Level Answers

41. 2, 3
42. No
43. 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
44. 2, 2, 2, 3
45. 2 × 2 × 3 = 12
46. 2, 2, 2, 3, 5
47. No
48. 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 72, 108, 144
49. 2, 3, 5
50. 23
51. 3, 5
52. No
53. 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 108, 144
54. 2, 3, 5
55. 2 × 2 × 2 = 8
56. 2, 2, 2, 5
57. No
58. 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 80, 120
59. 2, 3, 5
60. 47

I hope this helps you understand prime factors better! Remember, practice makes perfect! Happy studying!