Grade 5 Factoring Worksheet: Prime Factors (Numbers Under 500)

Sure! Let’s solve each problem step by step. The goal is to find the prime factorization of each number (i.e., break it down into a product of prime numbers) and then determine whether the original number is prime or not prime.

> 💡 Reminder: A prime number is a number greater than 1 that has exactly two distinct positive divisors: 1 and itself. If a number can be factored into primes other than just itself, it is not prime.

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1. 116

Start dividing by smallest primes:

- 116 ÷ 2 = 58 → divisible by 2
- 58 ÷ 2 = 29 → divisible by 2 again
- 29 is a prime number

✔ Prime factors: 2 × 2 × 29
✘ Is 116 prime? No

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2. 428

- 428 ÷ 2 = 214
- 214 ÷ 2 = 107
- 107 is a prime number

✔ Prime factors: 2 × 2 × 107
✘ Is 428 prime? No

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3. 87

- 87 ÷ 3 = 29 (since 8+7=15, divisible by 3)
- 29 is prime

✔ Prime factors: 3 × 29
✘ Is 87 prime? No

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4. 436

- 436 ÷ 2 = 218
- 218 ÷ 2 = 109
- 109 is prime

✔ Prime factors: 2 × 2 × 109
✘ Is 436 prime? No

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5. 68

- 68 ÷ 2 = 34
- 34 ÷ 2 = 17
- 17 is prime

✔ Prime factors: 2 × 2 × 17
✘ Is 68 prime? No

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6. 196

- 196 ÷ 2 = 98
- 98 ÷ 2 = 49
- 49 ÷ 7 = 7
- 7 is prime

✔ Prime factors: 2 × 2 × 7 × 7
✘ Is 196 prime? No

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7. 305

- 305 ends in 5 → divisible by 5
- 305 ÷ 5 = 61
- 61 is prime

✔ Prime factors: 5 × 61
✘ Is 305 prime? No

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8. 406

- 406 ÷ 2 = 203
- 203 ÷ 7 = 29 (since 7×29 = 203)
- Both 7 and 29 are prime

✔ Prime factors: 2 × 7 × 29
✘ Is 406 prime? No

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9. 202

- 202 ÷ 2 = 101
- 101 is prime

✔ Prime factors: 2 × 101
✘ Is 202 prime? No

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10. 499

Check if 499 is prime:

- Try dividing by primes up to √499 ≈ 22.3:
- Not divisible by 2 (odd)
- Not divisible by 3 (4+9+9=22, not divisible by 3)
- Not divisible by 5 (doesn’t end in 0 or 5)
- 7: 7×71=497 → 499-497=2 → not divisible
- 11: 11×45=495 → 499-495=4 → no
- 13: 13×38=494 → 499-494=5 → no
- 17: 17×29=493 → 499-493=6 → no
- 19: 19×26=494 → 499-494=5 → no
- 23: 23×21=483 → too small, 23×22=506 > 499

✔ So, 499 is prime

✔ Prime factors: 499 (itself)
✔ Is 499 prime? Yes

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## ✔ Final Answers:

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

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Let me know if you’d like a visual tree diagram for any of these! 🌳