Grade 6 Math Worksheets: Factoring numbers to prime factors (0-500 ... - Free Printable

Let's solve the Grade 6 Factoring Worksheet step by step. The goal is to factor each number into its prime factors and determine whether the number is prime or not.

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🔍 What are Prime Factors?

Prime factors are the prime numbers that multiply together to give the original number. A prime number has only two factors: 1 and itself.

We'll use division by primes (2, 3, 5, 7, 11, etc.) to break down each number.

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Let’s go through each one:

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1. 162

- Divisible by 2? Yes → 162 ÷ 2 = 81
- 81 → divisible by 3 → 81 ÷ 3 = 27
- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1

So:
162 = 2 × 3 × 3 × 3 × 3 = 2 × 3⁴
→ Not prime

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2. 247

Check divisibility:
- Not even → not divisible by 2
- Sum of digits: 2+4+7=13 → not divisible by 3
- Doesn’t end in 0 or 5 → not divisible by 5
- Try 7: 247 ÷ 7 ≈ 35.28 → no
- Try 11: 2 - 4 + 7 = 5 → not divisible by 11
- Try 13: 13 × 19 = 247 → yes!

So:
247 = 13 × 19
→ Not prime

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3. 401

Check if prime:
- It's odd → not divisible by 2
- Sum: 4+0+1=5 → not divisible by 3
- Doesn't end in 0 or 5 → not divisible by 5
- Try 7: 7×57=399 → 401−399=2 → not divisible
- 11: 4−0+1=5 → not divisible
- 13: 13×30=390 → 401−390=11 → not divisible
- 17: 17×23=391 → 401−391=10 → no
- 19: 19×21=399 → 401−399=2 → no
- 23: 23×17=391 → already checked

Try √401 ≈ 20 → check primes up to 19 — none divide it.

✔ 401 is a prime number
→ 401 = 401 (prime)

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4. 205

Ends in 5 → divisible by 5
205 ÷ 5 = 41

41 is a prime number.

So:
205 = 5 × 41
→ Not prime

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5. 373

Check if prime:
- Odd → not divisible by 2
- Sum: 3+7+3=13 → not divisible by 3
- Doesn't end in 0/5 → not divisible by 5
- Try 7: 7×53=371 → 373−371=2 → no
- 11: 3−7+3=−1 → not divisible
- 13: 13×28=364 → 373−364=9 → no
- 17: 17×21=357 → 373−357=16 → no
- 19: 19×19=361 → 373−361=12 → no
- 23: 23×16=368 → 373−368=5 → no

√373 ≈ 19.3 → check up to 19 — none divide it.

✔ 373 is a prime number
→ 373 = 373 (prime)

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6. 194

Even → divisible by 2
194 ÷ 2 = 97

97 is a prime number.

So:
194 = 2 × 97
→ Not prime

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7. 40

Even → ÷2 = 20
20 ÷ 2 = 10
10 ÷ 2 = 5
5 ÷ 5 = 1

So:
40 = 2 × 2 × 2 × 5 = 2³ × 5
→ Not prime

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8. 354

Even → ÷2 = 177
177: sum = 1+7+7=15 → divisible by 3 → 177 ÷ 3 = 59
59 is prime.

So:
354 = 2 × 3 × 59
→ Not prime

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9. 281

Odd → not divisible by 2
Sum: 2+8+1=11 → not divisible by 3
Doesn’t end in 0/5 → not divisible by 5
Try 7: 7×40=280 → 281−280=1 → no
11: 2−8+1=−5 → no
13: 13×21=273 → 281−273=8 → no
17: 17×16=272 → 281−272=9 → no
19: 19×14=266 → 281−266=15 → no
23: 23×12=276 → 281−276=5 → no

√281 ≈ 16.7 → check up to 16 → all done.

✔ 281 is a prime number
→ 281 = 281 (prime)

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10. 69

Odd → not divisible by 2
Sum: 6+9=15 → divisible by 3 → 69 ÷ 3 = 23
23 is prime.

So:
69 = 3 × 23
→ Not prime

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11. 133

Odd → not divisible by 2
Sum: 1+3+3=7 → not divisible by 3
Not divisible by 5
Try 7: 7×19 = 133 → yes!

So:
133 = 7 × 19
→ Not prime

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12. 92

Even → ÷2 = 46
46 ÷ 2 = 23
23 is prime.

So:
92 = 2 × 2 × 23 = 2² × 23
→ Not prime

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13. 450

Even → ÷2 = 225
225 → ends in 5 → ÷5 = 45
45 ÷ 5 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

So:
450 = 2 × 5 × 5 × 3 × 3 = 2 × 3² × 5²
→ Not prime

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14. 436

Even → ÷2 = 218
218 ÷ 2 = 109
109: check if prime
- Odd → not divisible by 2
- Sum: 1+0+9=10 → not divisible by 3
- Not divisible by 5
- Try 7: 7×15=105 → 109−105=4 → no
- 11: 1−0+9=10 → no
- 13: 13×8=104 → 109−104=5 → no
- √109 ≈ 10.4 → check up to 10 → done

✔ 109 is prime

So:
436 = 2 × 2 × 109 = 2² × 109
→ Not prime

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15. 367

Check if prime:
- Odd → not divisible by 2
- Sum: 3+6+7=16 → not divisible by 3
- Not divisible by 5
- Try 7: 7×52=364 → 367−364=3 → no
- 11: 3−6+7=4 → no
- 13: 13×28=364 → 367−364=3 → no
- 17: 17×21=357 → 367−357=10 → no
- 19: 19×19=361 → 367−361=6 → no
- 23: 23×15=345 → 367−345=22 → no

√367 ≈ 19.1 → check up to 19 → none divide it.

✔ 367 is a prime number
→ 367 = 367 (prime)

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16. 192

Even → ÷2 = 96
÷2 = 48
÷2 = 24
÷2 = 12
÷2 = 6
÷2 = 3
÷3 = 1

So:
192 = 2 × 2 × 2 × 2 × 2 × 2 × 3 = 2⁶ × 3
→ Not prime

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17. 190

Even → ÷2 = 95
95 → ends in 5 → ÷5 = 19
19 is prime.

So:
190 = 2 × 5 × 19
→ Not prime

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18. 94

Even → ÷2 = 47
47 is a prime number.

So:
94 = 2 × 47
→ Not prime

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19. 118

Even → ÷2 = 59
59 is prime.

So:
118 = 2 × 59
→ Not prime

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20. 112

Even → ÷2 = 56
÷2 = 28
÷2 = 14
÷2 = 7
7 is prime.

So:
112 = 2 × 2 × 2 × 2 × 7 = 2⁴ × 7
→ Not prime

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## ✔ Final Answers:

| Number | Prime Factorization | Is it Prime? |
|--------|----------------------|--------------|
| 1. 162 | 2 × 3⁴ | No |
| 2. 247 | 13 × 19 | No |
| 3. 401 | 401 | Yes |
| 4. 205 | 5 × 41 | No |
| 5. 373 | 373 | Yes |
| 6. 194 | 2 × 97 | No |
| 7. 40 | 2³ × 5 | No |
| 8. 354 | 2 × 3 × 59 | No |
| 9. 281 | 281 | Yes |
| 10. 69 | 3 × 23 | No |
| 11. 133 | 7 × 19 | No |
| 12. 92 | 2² × 23 | No |
| 13. 450 | 2 × 3² × 5² | No |
| 14. 436 | 2² × 109 | No |
| 15. 367 | 367 | Yes |
| 16. 192 | 2⁶ × 3 | No |
| 17. 190 | 2 × 5 × 19 | No |
| 18. 94 | 2 × 47 | No |
| 19. 118 | 2 × 59 | No |
| 20. 112 | 2⁴ × 7 | No |

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🟩 Summary:

The prime numbers in the list are:
401, 373, 281, 367

All others are composite and have been factored into primes.

Let me know if you'd like this as a printable answer sheet!