Grade 5 Factoring Worksheet: List the prime factors for each number under 500.

Explanation:
We need to find the prime factors of each number — that means breaking each number down into a product of only prime numbers (like 2, 3, 5, 7, 11, etc.). Then we’ll also say whether the original number is prime (only divisible by 1 and itself) or not.

Let’s go one by one:

1. 116
- Even → divisible by 2: 116 ÷ 2 = 58
- 58 ÷ 2 = 29
- 29 is prime.
So: 116 = 2 × 2 × 29 = 2² × 29
Not prime.

2. 428
- Even → ÷2 = 214
- 214 ÷ 2 = 107
- 107 is prime (check: not divisible by 2,3,5,7,11 — 11×9=99, 11×10=110 >107; √107 ≈10.3, so only need to test primes ≤10).
So: 428 = 2² × 107
Not prime.

3. 87
- Sum of digits: 8+7=15 → divisible by 3
- 87 ÷ 3 = 29
- 29 is prime.
So: 87 = 3 × 29
Not prime.

4. 436
- Even → ÷2 = 218
- 218 ÷ 2 = 109
- 109 is prime (√109 ≈10.4; test 2,3,5,7,11 — none divide it).
So: 436 = 2² × 109
Not prime.

5. 68
- Even → ÷2 = 34
- 34 ÷ 2 = 17
- 17 is prime.
So: 68 = 2² × 17
Not prime.

6. 196
- Even → ÷2 = 98
- 98 ÷ 2 = 49
- 49 = 7 × 7
So: 196 = 2 × 2 × 7 × 7 = 2² × 7²
Not prime.

7. 305
- Ends in 5 → divisible by 5: 305 ÷ 5 = 61
- 61 is prime.
So: 305 = 5 × 61
Not prime.

8. 406
- Even → ÷2 = 203
- 203: try 7 → 7×29 = 203 (since 7×28=196, +7=203)
- 29 is prime.
So: 406 = 2 × 7 × 29
Not prime.

9. 202
- Even → ÷2 = 101
- 101 is prime (√101≈10; test primes ≤10: none divide it).
So: 202 = 2 × 101
Not prime.

10. 499
- Check if prime:
Try dividing by small primes:
- Not even → not divisible by 2
- Sum digits: 4+9+9 = 22 → not divisible by 3
- Doesn’t end in 0 or 5 → not divisible by 5
- 7? 7×71 = 497, 7×72 = 504 → no
- 11? 11×45 = 495, 11×46 = 506 → no
- 13? 13×38 = 494, 13×39 = 507 → no
- 17? 17×29 = 493, 17×30 = 510 → no
- 19? 19×26 = 494, 19×27 = 513 → no
- 23? 23×21 = 483, 23×22 = 506 → no
- √499 ≈ 22.3, so we only need to test up to 23 — done.
So 499 is prime → its only prime factor is itself: 499

Now write each answer as requested: list prime factors (in multiplication form), and note if the number is prime.

Final Answer:
1. 116 = 2 × 2 × 29 (Not prime)
2. 428 = 2 × 2 × 107 (Not prime)
3. 87 = 3 × 29 (Not prime)
4. 436 = 2 × 2 × 109 (Not prime)
5. 68 = 2 × 2 × 17 (Not prime)
6. 196 = 2 × 2 × 7 × 7 (Not prime)
7. 305 = 5 × 61 (Not prime)
8. 406 = 2 × 7 × 29 (Not prime)
9. 202 = 2 × 101 (Not prime)
10. 499 = 499 (Prime)