Printable primary math worksheet for math grades 1 to 6 based on ... - Free Printable

Let's solve the prime factorization problems step by step. Prime factorization means expressing a number as a product of prime numbers (numbers divisible only by 1 and themselves).

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1. 64

We are given:
64 = 2 × 2 × ___

We know:
- 64 ÷ 2 = 32
- 32 ÷ 2 = 16
- 16 ÷ 2 = 8
- 8 ÷ 2 = 4
- 4 ÷ 2 = 2
- 2 ÷ 2 = 1

So, 64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁶

✔ Answer: 64 = 2 × 2 × 2 × 2 × 2 × 2

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2. 210

Break it down:
- 210 is even → divide by 2: 210 ÷ 2 = 105
- 105 ends in 5 → divisible by 5: 105 ÷ 5 = 21
- 21 = 3 × 7

So: 210 = 2 × 5 × 3 × 7
(All primes)

✔ Answer: 2 × 3 × 5 × 7

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3. 250

- Ends in 0 → divisible by 10 → 250 = 10 × 25
- But better to break into primes:
- 250 ÷ 2 = 125
- 125 ÷ 5 = 25
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1

So: 2 × 5 × 5 × 5 = 2 × 5³

✔ Answer: 2 × 5 × 5 × 5

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4. 375

- Ends in 5 → divisible by 5
- 375 ÷ 5 = 75
- 75 ÷ 5 = 15
- 15 ÷ 5 = 3
- 3 ÷ 3 = 1

So: 5 × 5 × 5 × 3 = 3 × 5³

✔ Answer: 3 × 5 × 5 × 5

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5. 125

- 125 ÷ 5 = 25
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1

So: 5 × 5 × 5 = 5³

✔ Answer: 5 × 5 × 5

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6. 250 (again)

Already done above.

✔ Answer: 2 × 5 × 5 × 5

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7. 350

- Even → ÷2 = 175
- 175 ÷ 5 = 35
- 35 ÷ 5 = 7
- 7 is prime

So: 2 × 5 × 5 × 7 = 2 × 5² × 7

✔ Answer: 2 × 5 × 5 × 7

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8. 98

- Even → ÷2 = 49
- 49 = 7 × 7

So: 2 × 7 × 7 = 2 × 7²

✔ Answer: 2 × 7 × 7

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9. 295

- Ends in 5 → divisible by 5
- 295 ÷ 5 = 59
- 59 is a prime number (not divisible by 2,3,5,7… up to √59 ≈ 7.6)

So: 5 × 59

✔ Answer: 5 × 59

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10. 140

- Even → ÷2 = 70
- 70 ÷ 2 = 35
- 35 ÷ 5 = 7
- 7 is prime

So: 2 × 2 × 5 × 7 = 2² × 5 × 7

✔ Answer: 2 × 2 × 5 × 7

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11. 100

- 100 = 10 × 10 = (2×5) × (2×5) = 2² × 5²

Or:
- 100 ÷ 2 = 50
- 50 ÷ 2 = 25
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1

So: 2 × 2 × 5 × 5

✔ Answer: 2 × 2 × 5 × 5

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12. 175

- Ends in 5 → ÷5 = 35
- 35 ÷ 5 = 7
- 7 is prime

So: 5 × 5 × 7 = 5² × 7

✔ Answer: 5 × 5 × 7

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13. 200

- Even → ÷2 = 100
- 100 → we already did: 2 × 2 × 5 × 5

So: 2 × 2 × 2 × 5 × 5 = 2³ × 5²

✔ Answer: 2 × 2 × 2 × 5 × 5

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14. 525

- Ends in 5 → ÷5 = 105
- 105 ÷ 5 = 21
- 21 = 3 × 7

So: 5 × 5 × 3 × 7 = 3 × 5² × 7

✔ Answer: 3 × 5 × 5 × 7

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15. 364

- Even → ÷2 = 182
- 182 ÷ 2 = 91
- 91 → check divisibility:
- Not divisible by 2, 3, or 5
- 91 ÷ 7 = 13 → yes! 7 × 13 = 91

So: 2 × 2 × 7 × 13

✔ Answer: 2 × 2 × 7 × 13

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16. 230

- Even → ÷2 = 115
- 115 ÷ 5 = 23
- 23 is prime

So: 2 × 5 × 23

✔ Answer: 2 × 5 × 23

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17. 88

- Even → ÷2 = 44
- 44 ÷ 2 = 22
- 22 ÷ 2 = 11
- 11 is prime

So: 2 × 2 × 2 × 11 = 2³ × 11

✔ Answer: 2 × 2 × 2 × 11

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18. 110

- Even → ÷2 = 55
- 55 ÷ 5 = 11
- 11 is prime

So: 2 × 5 × 11

✔ Answer: 2 × 5 × 11

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✔ Final Answers:

| Number | Prime Factorization |
|--------|---------------------|
| 64 | 2 × 2 × 2 × 2 × 2 × 2 |
| 210 | 2 × 3 × 5 × 7 |
| 250 | 2 × 5 × 5 × 5 |
| 375 | 3 × 5 × 5 × 5 |
| 125 | 5 × 5 × 5 |
| 250 | 2 × 5 × 5 × 5 |
| 350 | 2 × 5 × 5 × 7 |
| 98 | 2 × 7 × 7 |
| 295 | 5 × 59 |
| 140 | 2 × 2 × 5 × 7 |
| 100 | 2 × 2 × 5 × 5 |
| 175 | 5 × 5 × 7 |
| 200 | 2 × 2 × 2 × 5 × 5 |
| 525 | 3 × 5 × 5 × 7 |
| 364 | 2 × 2 × 7 × 13 |
| 230 | 2 × 5 × 23 |
| 88 | 2 × 2 × 2 × 11 |
| 110 | 2 × 5 × 11 |

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