Prime Factorization Worksheets - 15 Worksheets Library - Free Printable

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 by 2:
250 ÷ 2 = 125 → 2 is a prime factor
125 is odd, so not divisible by 2. Try 5:
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1

So:
250 = 2 × 5 × 5 × 5 = 2 × 5³
→ Prime factors: 2, 5

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2. 600

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

So:
600 = 2 × 2 × 2 × 3 × 5 × 5 = 2³ × 3 × 5²
→ Prime factors: 2, 3, 5

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3. 100

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

So:
100 = 2 × 2 × 5 × 5 = 2² × 5²
→ Prime factors: 2, 5

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4. 120

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

So:
120 = 2 × 2 × 2 × 3 × 5 = 2³ × 3 × 5
→ Prime factors: 2, 3, 5

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5. 350

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

So:
350 = 2 × 5 × 5 × 7 = 2 × 5² × 7
→ Prime factors: 2, 5, 7

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6. 550

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

So:
550 = 2 × 5 × 5 × 11 = 2 × 5² × 11
→ Prime factors: 2, 5, 11

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7. 480

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

So:
480 = 2⁵ × 3 × 5
→ Prime factors: 2, 3, 5

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8. 650

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

So:
650 = 2 × 5 × 5 × 13 = 2 × 5² × 13
→ Prime factors: 2, 5, 13

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9. 700

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

So:
700 = 2 × 2 × 5 × 5 × 7 = 2² × 5² × 7
→ Prime factors: 2, 5, 7

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10. 360

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

So:
360 = 2³ × 3² × 5
→ Prime factors: 2, 3, 5

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11. 450

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

So:
450 = 2 × 3² × 5²
→ Prime factors: 2, 3, 5

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12. 525

525 ÷ 3 = 175 (since 5+2+5=12, divisible by 3)
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1

So:
525 = 3 × 5 × 5 × 7 = 3 × 5² × 7
→ Prime factors: 3, 5, 7

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13. 400

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

So:
400 = 2⁴ × 5²
→ Prime factors: 2, 5

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14. 180

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

So:
180 = 2² × 3² × 5
→ Prime factors: 2, 3, 5

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15. 320

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

So:
320 = 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, even if they appear multiple times. For example, 100 = 2² × 5² → prime factors are 2 and 5.

Let me know if you'd like this in a printable format or want the full factor tree diagrams!