Practice finding prime factors with this comprehensive math worksheet featuring 15 different numbers.

Let's solve each of these problems step by step. The task is to list all the prime factors for each number. Prime factorization means breaking down a number into its prime number components, which are numbers greater than 1 that have no positive divisors other than 1 and themselves (e.g., 2, 3, 5, 7, 11, etc.).

We'll use division by primes (starting with the smallest) until we reach 1.

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1. 250

Divide:
- 250 ÷ 2 = 125 → 2 is a prime factor
- 125 ÷ 5 = 25 → 5 is a prime factor
- 25 ÷ 5 = 5 → 5 again
- 5 ÷ 5 = 1 → 5 again

So: 2 × 5 × 5 × 5 = 2 × 5³

✔ Prime factors: 2, 5

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2. 600

- 600 ÷ 2 = 300 → 2
- 300 ÷ 2 = 150 → 2
- 150 ÷ 2 = 75 → 2
- 75 ÷ 3 = 25 → 3
- 25 ÷ 5 = 5 → 5
- 5 ÷ 5 = 1 → 5

So: 2³ × 3 × 5²

✔ Prime factors: 2, 3, 5

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3. 100

- 100 ÷ 2 = 50 → 2
- 50 ÷ 2 = 25 → 2
- 25 ÷ 5 = 5 → 5
- 5 ÷ 5 = 1 → 5

So: 2² × 5²

✔ Prime factors: 2, 5

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4. 120

- 120 ÷ 2 = 60 → 2
- 60 ÷ 2 = 30 → 2
- 30 ÷ 2 = 15 → 2
- 15 ÷ 3 = 5 → 3
- 5 ÷ 5 = 1 → 5

So: 2³ × 3 × 5

✔ Prime factors: 2, 3, 5

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5. 350

- 350 ÷ 2 = 175 → 2
- 175 ÷ 5 = 35 → 5
- 35 ÷ 5 = 7 → 5
- 7 ÷ 7 = 1 → 7

So: 2 × 5² × 7

✔ Prime factors: 2, 5, 7

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6. 550

- 550 ÷ 2 = 275 → 2
- 275 ÷ 5 = 55 → 5
- 55 ÷ 5 = 11 → 5
- 11 ÷ 11 = 1 → 11

So: 2 × 5² × 11

✔ Prime factors: 2, 5, 11

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7. 480

- 480 ÷ 2 = 240 → 2
- 240 ÷ 2 = 120 → 2
- 120 ÷ 2 = 60 → 2
- 60 ÷ 2 = 30 → 2
- 30 ÷ 2 = 15 → 2
- 15 ÷ 3 = 5 → 3
- 5 ÷ 5 = 1 → 5

So: 2⁵ × 3 × 5

✔ Prime factors: 2, 3, 5

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8. 650

- 650 ÷ 2 = 325 → 2
- 325 ÷ 5 = 65 → 5
- 65 ÷ 5 = 13 → 5
- 13 ÷ 13 = 1 → 13

So: 2 × 5² × 13

✔ Prime factors: 2, 5, 13

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9. 700

- 700 ÷ 2 = 350 → 2
- 350 ÷ 2 = 175 → 2
- 175 ÷ 5 = 35 → 5
- 35 ÷ 5 = 7 → 5
- 7 ÷ 7 = 1 → 7

So: 2² × 5² × 7

✔ Prime factors: 2, 5, 7

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10. 360

- 360 ÷ 2 = 180 → 2
- 180 ÷ 2 = 90 → 2
- 90 ÷ 2 = 45 → 2
- 45 ÷ 3 = 15 → 3
- 15 ÷ 3 = 5 → 3
- 5 ÷ 5 = 1 → 5

So: 2³ × 3² × 5

✔ Prime factors: 2, 3, 5

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11. 450

- 450 ÷ 2 = 225 → 2
- 225 ÷ 3 = 75 → 3
- 75 ÷ 3 = 25 → 3
- 25 ÷ 5 = 5 → 5
- 5 ÷ 5 = 1 → 5

So: 2 × 3² × 5²

✔ Prime factors: 2, 3, 5

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12. 525

- 525 ÷ 3 = 175 → 3
- 175 ÷ 5 = 35 → 5
- 35 ÷ 5 = 7 → 5
- 7 ÷ 7 = 1 → 7

So: 3 × 5² × 7

✔ Prime factors: 3, 5, 7

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13. 400

- 400 ÷ 2 = 200 → 2
- 200 ÷ 2 = 100 → 2
- 100 ÷ 2 = 50 → 2
- 50 ÷ 2 = 25 → 2
- 25 ÷ 5 = 5 → 5
- 5 ÷ 5 = 1 → 5

So: 2⁴ × 5²

✔ Prime factors: 2, 5

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14. 180

- 180 ÷ 2 = 90 → 2
- 90 ÷ 2 = 45 → 2
- 45 ÷ 3 = 15 → 3
- 15 ÷ 3 = 5 → 3
- 5 ÷ 5 = 1 → 5

So: 2² × 3² × 5

✔ Prime factors: 2, 3, 5

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15. 320

- 320 ÷ 2 = 160 → 2
- 160 ÷ 2 = 80 → 2
- 80 ÷ 2 = 40 → 2
- 40 ÷ 2 = 20 → 2
- 20 ÷ 2 = 10 → 2
- 10 ÷ 2 = 5 → 2
- 5 ÷ 5 = 1 → 5

So: 2⁶ × 5

✔ Prime factors: 2, 5

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✔ Final Answers:

1. 250: 2, 5
2. 600: 2, 3, 5
3. 100: 2, 5
4. 120: 2, 3, 5
5. 350: 2, 5, 7
6. 550: 2, 5, 11
7. 480: 2, 3, 5
8. 650: 2, 5, 13
9. 700: 2, 5, 7
10. 360: 2, 3, 5
11. 450: 2, 3, 5
12. 525: 3, 5, 7
13. 400: 2, 5
14. 180: 2, 3, 5
15. 320: 2, 5

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💡 Note: We list only the distinct prime factors unless otherwise asked for full factorization (with exponents). Since the question says "list all the prime factors", and doesn't specify repetition, we usually list unique prime factors. But if you're required to show all (including repeated), then include them as many times as they appear. However, in standard practice, "prime factors" refers to the set of distinct primes dividing the number.

So final answer format (as per typical expectations):

> 1. 2, 5
> 2. 2, 3, 5
> 3. 2, 5
> 4. 2, 3, 5
> 5. 2, 5, 7
> 6. 2, 5, 11
> 7. 2, 3, 5
> 8. 2, 5, 13
> 9. 2, 5, 7
> 10. 2, 3, 5
> 11. 2, 3, 5
> 12. 3, 5, 7
> 13. 2, 5
> 14. 2, 3, 5
> 15. 2, 5

✔ All done!