Factoring numbers 1-100 to prime factors worksheet for Grade 6 students.

Let's solve the Grade 6 Factoring Worksheet step by step. The goal is to factor each number from 1 to 100 into its prime factors.

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🔍 What are Prime Factors?

Prime factors are the prime numbers that multiply together to give the original number. For example:
- $ 12 = 2 \times 2 \times 3 = 2^2 \times 3 $

We’ll use prime factorization for each number.

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✔ Solutions:

1. 98
$ 98 \div 2 = 49 $ → $ 49 = 7 \times 7 $
So, $ 98 = 2 \times 7 \times 7 = 2 \times 7^2 $

2. 40
$ 40 \div 2 = 20 $ → $ 20 \div 2 = 10 $ → $ 10 \div 2 = 5 $
So, $ 40 = 2 \times 2 \times 2 \times 5 = 2^3 \times 5 $

3. 83
Check if divisible by any prime less than √83 (~9.1): 2, 3, 5, 7
- Not divisible by any → 83 is a prime number
So, $ 83 = 83 $

4. 2
$ 2 $ is already a prime number
So, $ 2 = 2 $

5. 87
$ 87 \div 3 = 29 $ (since 8+7=15 divisible by 3)
$ 29 $ is prime
So, $ 87 = 3 \times 29 $

6. 46
$ 46 \div 2 = 23 $ → $ 23 $ is prime
So, $ 46 = 2 \times 23 $

7. 80
$ 80 \div 2 = 40 $ → $ 40 \div 2 = 20 $ → $ 20 \div 2 = 10 $ → $ 10 \div 2 = 5 $
So, $ 80 = 2 \times 2 \times 2 \times 2 \times 5 = 2^4 \times 5 $

8. 89
Check divisibility: not divisible by 2, 3, 5, 7 → 89 is prime
So, $ 89 = 89 $

9. 53
Check primes up to √53 (~7.3): 2, 3, 5, 7 → not divisible
So, $ 53 = 53 $ (prime)

10. 50
$ 50 \div 2 = 25 $ → $ 25 = 5 \times 5 $
So, $ 50 = 2 \times 5 \times 5 = 2 \times 5^2 $

11. 69
$ 69 \div 3 = 23 $ (6+9=15 divisible by 3)
$ 23 $ is prime
So, $ 69 = 3 \times 23 $

12. 82
$ 82 \div 2 = 41 $ → $ 41 $ is prime
So, $ 82 = 2 \times 41 $

13. 67
Check primes up to √67 (~8.2): 2, 3, 5, 7 → not divisible
So, $ 67 = 67 $ (prime)

14. 76
$ 76 \div 2 = 38 $ → $ 38 \div 2 = 19 $ → $ 19 $ is prime
So, $ 76 = 2 \times 2 \times 19 = 2^2 \times 19 $

15. 49
$ 49 = 7 \times 7 = 7^2 $

16. 32
$ 32 = 2 \times 2 \times 2 \times 2 \times 2 = 2^5 $

17. 47
Check divisibility: not divisible by 2, 3, 5, 7 → 47 is prime
So, $ 47 = 47 $

18. 3
Already a prime number → $ 3 = 3 $

19. 94
$ 94 \div 2 = 47 $ → $ 47 $ is prime
So, $ 94 = 2 \times 47 $

20. 9
$ 9 = 3 \times 3 = 3^2 $

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✔ Final Answers:

1. $ 98 = 2 \times 7^2 $
2. $ 40 = 2^3 \times 5 $
3. $ 83 = 83 $
4. $ 2 = 2 $
5. $ 87 = 3 \times 29 $
6. $ 46 = 2 \times 23 $
7. $ 80 = 2^4 \times 5 $
8. $ 89 = 89 $
9. $ 53 = 53 $
10. $ 50 = 2 \times 5^2 $
11. $ 69 = 3 \times 23 $
12. $ 82 = 2 \times 41 $
13. $ 67 = 67 $
14. $ 76 = 2^2 \times 19 $
15. $ 49 = 7^2 $
16. $ 32 = 2^5 $
17. $ 47 = 47 $
18. $ 3 = 3 $
19. $ 94 = 2 \times 47 $
20. $ 9 = 3^2 $

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🧠 Tips for Prime Factorization:

- Always divide by the smallest prime first (2, then 3, 5, 7, etc.)
- Stop when you reach a prime number.
- Use exponents for repeated factors.

Let me know if you’d like this as a printable PDF or want explanations for specific problems!