Let's solve each problem by finding
all the prime factors of each number. Prime factorization means breaking down a number into its smallest prime numbers that multiply together to give the original number.
We'll go through each one step by step:
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1) 76
- 76 ÷ 2 = 38 → 2 is a prime factor
- 38 ÷ 2 = 19 → 2 again
- 19 is a prime number
✔ Prime factors: 2, 2, 19 or
2² × 19
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2) 18
- 18 ÷ 2 = 9 → 2 is a prime factor
- 9 ÷ 3 = 3 → 3 is a prime factor
- 3 ÷ 3 = 1 → 3 again
✔ Prime factors: 2, 3, 3 or
2 × 3²
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3) 56
- 56 ÷ 2 = 28 → 2
- 28 ÷ 2 = 14 → 2
- 14 ÷ 2 = 7 → 2
- 7 is prime
✔ Prime factors: 2, 2, 2, 7 or
2³ × 7
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4) 58
- 58 ÷ 2 = 29 → 2
- 29 is a prime number
✔ Prime factors: 2, 29
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5) 25
- 25 ÷ 5 = 5 → 5
- 5 ÷ 5 = 1 → 5 again
✔ Prime factors: 5, 5 or
5²
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6) 80
- 80 ÷ 2 = 40 → 2
- 40 ÷ 2 = 20 → 2
- 20 ÷ 2 = 10 → 2
- 10 ÷ 2 = 5 → 2
- 5 is prime
✔ Prime factors: 2, 2, 2, 2, 5 or
2⁴ × 5
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7) 68
- 68 ÷ 2 = 34 → 2
- 34 ÷ 2 = 17 → 2
- 17 is prime
✔ Prime factors: 2, 2, 17 or
2² × 17
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8) 36
- 36 ÷ 2 = 18 → 2
- 18 ÷ 2 = 9 → 2
- 9 ÷ 3 = 3 → 3
- 3 ÷ 3 = 1 → 3
✔ Prime factors: 2, 2, 3, 3 or
2² × 3²
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9) 26
- 26 ÷ 2 = 13 → 2
- 13 is prime
✔ Prime factors: 2, 13
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10) 22
- 22 ÷ 2 = 11 → 2
- 11 is prime
✔ Prime factors: 2, 11
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11) 12
- 12 ÷ 2 = 6 → 2
- 6 ÷ 2 = 3 → 2
- 3 is prime
✔ Prime factors: 2, 2, 3 or
2² × 3
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12) 52
- 52 ÷ 2 = 26 → 2
- 26 ÷ 2 = 13 → 2
- 13 is prime
✔ Prime factors: 2, 2, 13 or
2² × 13
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13) 78
- 78 ÷ 2 = 39 → 2
- 39 ÷ 3 = 13 → 3
- 13 is prime
✔ Prime factors: 2, 3, 13
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14) 32
- 32 ÷ 2 = 16 → 2
- 16 ÷ 2 = 8 → 2
- 8 ÷ 2 = 4 → 2
- 4 ÷ 2 = 2 → 2
- 2 ÷ 2 = 1 → 2
✔ Prime factors: 2, 2, 2, 2, 2 or
2⁵
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15) 51
- 51 ÷ 3 = 17 → 3
- 17 is prime
✔ Prime factors: 3, 17
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✔ Final Answers:
1) 76 →
2, 2, 19
2) 18 →
2, 3, 3
3) 56 →
2, 2, 2, 7
4) 58 →
2, 29
5) 25 →
5, 5
6) 80 →
2, 2, 2, 2, 5
7) 68 →
2, 2, 17
8) 36 →
2, 2, 3, 3
9) 26 →
2, 13
10) 22 →
2, 11
11) 12 →
2, 2, 3
12) 52 →
2, 2, 13
13) 78 →
2, 3, 13
14) 32 →
2, 2, 2, 2, 2
15) 51 →
3, 17
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You can write these in the blank lines on the worksheet as
lists of prime numbers, separated by commas.
Let me know if you'd like this formatted for printing or copying!
Parent Tip: Review the logic above to help your child master the concept of prime factorization worksheet 6th grade.
