Year 8 Maths: Factors Multiples and Primes

Introduction

Welcome to our lesson on Factors, Multiples, and Prime numbers! Today, we will explore these important concepts in maths. Let’s break them down step by step.

What are Factors?

Factors are the numbers you can multiply together to get another number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because:

• $1 \times 12 = 12$
• $2 \times 6 = 12$
• $3 \times 4 = 12$

Key Rule for Factors

A factor is always less than or equal to the number.

Tips for Finding Factors

1. Start with 1 and the number itself.
2. Check numbers in between to see if they divide evenly (no remainders).

What are Multiples?

Multiples are what you get when you multiply a number by an integer (whole number). For example, the first few multiples of 3 are:

• $3 \times 1 = 3$
• $3 \times 2 = 6$
• $3 \times 3 = 9$
• $3 \times 4 = 12$
• $3 \times 5 = 15$

So, the multiples of 3 are 3, 6, 9, 12, and 15.

Key Rule for Multiples

A multiple is always greater than or equal to the number.

Tips for Finding Multiples

1. Start from the number itself and keep adding the number repeatedly.
2. Use a multiplication table for help.

What are Prime Numbers?

Prime numbers are numbers greater than 1 that have no factors other than 1 and themselves. This means they cannot be divided evenly by any other numbers. Some examples of prime numbers are:

• 2 (factors: 1, 2)
• 3 (factors: 1, 3)
• 5 (factors: 1, 5)
• 7 (factors: 1, 7)
• 11 (factors: 1, 11)

Key Rule for Prime Numbers

The only even prime number is 2. All other even numbers can be divided by 2, which means they have factors other than 1 and themselves.

Tips for Identifying Prime Numbers

1. Check if the number can be divided by any other numbers (besides 1 and itself).
2. Use a list of known prime numbers to help you.

Summary

• Factors are numbers that can multiply to create another number.
• Multiples are what you get from multiplying a number by whole numbers.
• Prime numbers have only two factors: 1 and themselves.

Now, let’s test your understanding with some questions!

Questions

Easy Level (1-20)

1. What are the factors of 10?
2. What are the first three multiples of 4?
3. Is 6 a prime number? Why or why not?
4. What are the factors of 15?
5. List the first five multiples of 2.
6. Is 5 a prime number? Explain.
7. What are the factors of 8?
8. What is the 5th multiple of 3?
9. Is 9 a prime number? Why or why not?
10. What are the factors of 12?
11. List the multiples of 5 up to 25.
12. What is the smallest prime number?
13. What are the factors of 14?
14. List the first four multiples of 7.
15. Is 1 a prime number? Explain your answer.
16. What are the factors of 18?
17. What is the 3rd multiple of 6?
18. Is 10 a prime number? Why or why not?
19. What are the factors of 20?
20. List the first three multiples of 9.

Medium Level (21-40)

21. What are the factors of 30?
22. List the first five multiples of 8.
23. Identify all prime numbers between 1 and 20.
24. What are the factors of 21?
25. What is the 6th multiple of 4?
26. Is 12 a prime number? Why or why not?
27. What are the factors of 24?
28. List the multiples of 6 up to 36.
29. Identify if 15 is a prime number or not.
30. What are the factors of 28?
31. What is the 4th multiple of 5?
32. Are there any prime numbers greater than 20 and less than 30? Name them.
33. What are the factors of 35?
34. List the first three multiples of 11.
35. Is 22 a prime number? Explain your reasoning.
36. What are the factors of 36?
37. What is the 2nd multiple of 7?
38. Is 13 a prime number? Why or why not?
39. What are the factors of 16?
40. List the first five multiples of 10.

Hard Level (41-60)

41. What are the factors of 45?
42. List the first seven multiples of 3.
43. Are there any prime numbers between 30 and 40? Name them.
44. What are the factors of 50?
45. What is the 8th multiple of 12?
46. Is 25 a prime number? Justify your answer.
47. What are the factors of 100?
48. List the multiples of 9 up to 81.
49. Identify which numbers from 1 to 50 are prime.
50. What are the factors of 42?
51. What is the 5th multiple of 15?
52. Is 27 a prime number? Explain your answer.
53. What are the factors of 60?
54. List the first six multiples of 8.
55. Identify if 17 is a prime number or not.
56. What are the factors of 70?
57. What is the 3rd multiple of 14?
58. Are there any prime numbers between 40 and 50? Name them.
59. What are the factors of 81?
60. List the first four multiples of 13.

Answers

Easy Level Answers

1. 1, 2, 5, 10
2. 4, 8, 12
3. No, because it can be divided by 1, 2, 3, and 6.
4. 1, 3, 5, 15
5. 2, 4, 6, 8, 10
6. Yes, because its only factors are 1 and 5.
7. 1, 2, 4, 8
8. 15
9. No, because it can be divided by 1, 3, and 9.
10. 1, 2, 3, 4, 6, 12
11. 5, 10, 15, 20, 25
12. 2
13. 1, 2, 7, 14
14. 7, 14, 21, 28
15. No, because it can only be divided by itself.
16. 1, 2, 3, 6, 9, 18
17. 18
18. No, it can be divided by 1, 2, 5, and 10.
19. 1, 2, 4, 5, 10, 20
20. 9, 18, 27

Medium Level Answers

21. 1, 2, 3, 5, 6, 10, 15, 30
22. 8, 16, 24, 32, 40
23. 2, 3, 5, 7, 11, 13, 17, 19
24. 1, 3, 7, 21
25. 24
26. No, because it has factors other than 1 and 12.
27. 1, 2, 3, 4, 6, 8, 12, 24
28. 6, 12, 18, 24, 30, 36
29. No, because it has factors 1, 3, 5, and 15.
30. 1, 2, 4, 7, 14, 28
31. 25
32. 23, 29
33. 1, 5, 7, 35
34. 11, 22, 33
35. No, it can be divided by 1, 2, 11, and 22.
36. 1, 2, 3, 4, 6, 9, 12, 18, 36
37. 21
38. Yes, because its only factors are 1 and 17.
39. 1, 2, 4, 8, 16
40. 10, 20, 30, 40, 50

Hard Level Answers

41. 1, 3, 5, 9, 15, 45
42. 3, 6, 9, 12, 15, 18, 21
43. 31, 37
44. 1, 2, 5, 10, 25, 50
45. 96
46. No, it can be divided by 1, 5, and 25.
47. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
48. 9, 18, 27, 36, 45, 54, 63, 72, 81
49. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
50. 1, 2, 3, 6, 7, 14, 21, 42
51. 75
52. No, it can be divided by 1, 3, 9, and 27.
53. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
54. 8, 16, 24, 32, 40, 48
55. Yes, because its only factors are 1 and 17.
56. 1, 2, 4, 5, 7, 10, 14, 35, 70
57. 42
58. 41, 43, 47
59. 1, 3, 9, 27, 81
60. 13, 26, 39

Feel free to use these questions to practice. Good luck, and remember to ask questions if you’re unsure about anything!