Explanation:
We need to factor each number into its
prime factors — that means breaking it down into a product of prime numbers only (like 2, 3, 5, 7, 11, etc.).
Let’s go one by one:
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1 a. 34
- 34 is even → divisible by 2:
34 ÷ 2 = 17
- 17 is a prime number.
✔ So, 34 = 2 × 17
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1 b. 242
- 242 is even → divisible by 2:
242 ÷ 2 = 121
- 121 is not divisible by 2, 3, or 5. Try 11:
11 × 11 = 121
✔ So, 242 = 2 × 11 × 11 = 2 × 11²
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2 a. 451
- Not even, doesn’t end in 0 or 5 → not divisible by 2 or 5.
- Sum of digits: 4 + 5 + 1 = 10 → not divisible by 3.
- Try dividing by small primes:
- 451 ÷ 7 = 64.428… no
- 451 ÷ 11 = 41 → because 11 × 41 = 451 ✔️
- Check if 41 is prime: yes, it has no divisors other than 1 and itself.
✔ So, 451 = 11 × 41
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2 b. 247
- Not even, not divisible by 3 (2+4+7=13), not by 5.
- Try 7: 7 × 35 = 245 → 247 − 245 = 2 → not divisible
- Try 13: 13 × 19 = 247? Let's check:
13 × 19 = (10+3)×19 = 190 + 57 = 247 ✔️
- Both 13 and 19 are prime.
✔ So, 247 = 13 × 19
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3 a. 160
- Even → divide by 2 repeatedly:
160 ÷ 2 = 80
80 ÷ 2 = 40
40 ÷ 2 = 20
20 ÷ 2 = 10
10 ÷ 2 = 5
- Now 5 is prime.
So we divided by 2 five times: 2⁵ × 5
✔ 160 = 2⁵ × 5
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3 b. 309
- Sum of digits: 3 + 0 + 9 = 12 → divisible by 3
309 ÷ 3 = 103
- Is 103 prime? Check divisibility:
Not even, not divisible by 3 (1+0+3=4), not by 5, 7 (7×14=98, 7×15=105), 11 (11×9=99, 11×10=110), 13 (13×7=91, 13×8=104) → too big.
√103 ≈ 10.1, so only need to test primes ≤10: 2,3,5,7 — none divide 103.
✔ So 103 is prime.
Thus, 309 = 3 × 103
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Final Answer:
1 a. 2 × 17
1 b. 2 × 11²
2 a. 11 × 41
2 b. 13 × 19
3 a. 2⁵ × 5
3 b. 3 × 103
Parent Tip: Review the logic above to help your child master the concept of prime factorization worksheet grade 5.
