Practice Factoring Prime Numbers Worksheets - Free Printable

Let’s solve each problem step by step, finding the prime factors of each number and stating whether the number itself is prime.

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1. 119 = ?

We need to find the prime factors of 119.

- Check divisibility by small primes:
- 119 is odd, so not divisible by 2.
- Sum of digits: 1 + 1 + 9 = 11 → not divisible by 3.
- Doesn’t end in 0 or 5 → not divisible by 5.
- Try 7:
119 ÷ 7 = 17 → Yes! 7 × 17 = 119.

- Now check if 7 and 17 are prime:
- 7 is prime.
- 17 is prime.

✔ So, 119 = 7 × 17

→ Since 119 has factors other than 1 and itself, 119 is NOT prime.

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2. 48 = ?

Find prime factors of 48.

- Divide by smallest prime (2):
- 48 ÷ 2 = 24
- 24 ÷ 2 = 12
- 12 ÷ 2 = 6
- 6 ÷ 2 = 3
- 3 ÷ 3 = 1

So we divided by 2 four times, then by 3 once.

✔ So, 48 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3

→ Since 48 has more than two factors, 48 is NOT prime.

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3. 81 = ?

Find prime factors of 81.

- 81 is odd → not divisible by 2.
- Sum of digits: 8 + 1 = 9 → divisible by 3.
- 81 ÷ 3 = 27
- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1

So we divided by 3 four times.

✔ So, 81 = 3 × 3 × 3 × 3 = 3⁴

→ Since 81 has factors other than 1 and itself, 81 is NOT prime.

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## ✔ Final Answers:

1. 119 = 7 × 17 → NOT prime
2. 48 = 2 × 2 × 2 × 2 × 3 → NOT prime
3. 81 = 3 × 3 × 3 × 3 → NOT prime

*(Note: The example given — “83 is Prime” — is correct, since 83 has no divisors other than 1 and itself.)*