Prime factorization worksheet with six numbers to break down into prime factors using factor trees.

Let’s solve each problem step by step. We are finding the prime factors of each number — that means breaking the number down into prime numbers (numbers only divisible by 1 and themselves) that multiply together to give the original number.

We’ll use factor trees for each, then write the prime factors in multiplication form.

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Problem 1: 20

Start with 20.
Break it into two factors: 2 × 10 → 2 is prime, 10 is not.
Break 10 into 2 × 5 → both prime.

So:
20 = 2 × 2 × 5

✔ Prime Factors: 2 × 2 × 5 = 20

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Problem 2: 99

Start with 99.
Break into 3 × 33 → 3 is prime, 33 is not.
Break 33 into 3 × 11 → both prime.

So:
99 = 3 × 3 × 11

✔ Prime Factors: 3 × 3 × 11 = 99

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Problem 3: 45

Start with 45.
Break into 3 × 15 → 3 is prime, 15 is not.
Break 15 into 3 × 5 → both prime.

So:
45 = 3 × 3 × 5

✔ Prime Factors: 3 × 3 × 5 = 45

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Problem 4: 28

Start with 28.
Break into 2 × 14 → 2 is prime, 14 is not.
Break 14 into 2 × 7 → both prime.

So:
28 = 2 × 2 × 7

✔ Prime Factors: 2 × 2 × 7 = 28

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Problem 5: 52

Start with 52.
Break into 2 × 26 → 2 is prime, 26 is not.
Break 26 into 2 × 13 → both prime.

So:
52 = 2 × 2 × 13

✔ Prime Factors: 2 × 2 × 13 = 52

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Problem 6: 30

Start with 30.
Break into 2 × 15 → 2 is prime, 15 is not.
Break 15 into 3 × 5 → both prime.

So:
30 = 2 × 3 × 5

✔ Prime Factors: 2 × 3 × 5 = 30

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Final Answer:

1) 2 × 2 × 5 = 20
2) 3 × 3 × 11 = 99
3) 3 × 3 × 5 = 45
4) 2 × 2 × 7 = 28
5) 2 × 2 × 13 = 52
6) 2 × 3 × 5 = 30