Factor tree worksheet for practicing prime factorization with visual tree diagrams.

Let’s solve each factor tree step by step. Remember: a factor tree breaks down a number into its prime factors — numbers that can only be divided by 1 and themselves (like 2, 3, 5, 7, etc.). We multiply all the primes at the bottom to get back the original number.

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Problem 1: 35

We start with 35. What two numbers multiply to 35?
→ 5 × 7 = 35
Both 5 and 7 are prime → stop here.
So: 35 = 5 × 7

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Problem 2: 14

Start with 14.
→ 2 × 7 = 14
Both 2 and 7 are prime → done.
So: 14 = 2 × 7

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Problem 3: 33

Start with 33.
→ 3 × 11 = 33
Both 3 and 11 are prime → done.
So: 33 = 3 × 11

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Problem 4: 12

Start with 12. The tree shows it splits into ? and 6.
What times 6 equals 12? → 2 × 6 = 12
Now break down 6: 6 = 2 × 3 (both prime)
So full breakdown: 12 = 2 × 2 × 3
Answer line says: 12 = _ × _ × _ → fill in: 2 × 2 × 3

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Problem 5: 30

Tree shows 30 splits into ? and 15.
What times 15 is 30? → 2 × 15 = 30
Break down 15: 15 = 3 × 5 (both prime)
So: 30 = 2 × 3 × 5
Answer line: 30 = _ × _ × _ → 2 × 3 × 5

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Problem 6: 27

Tree shows 27 splits into ? and 9.
What times 9 is 27? → 3 × 9 = 27
Break down 9: 9 = 3 × 3 (both prime)
So: 27 = 3 × 3 × 3
Answer line: 27 = _ × _ × _ → 3 × 3 × 3

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Problem 7: 20

Tree shows 20 splits into ? and ?. Let’s pick easy factors: 4 × 5 = 20
But 4 is not prime → break 4 into 2 × 2
So: 20 = 2 × 2 × 5
Answer line: 20 = _ × _ × _ → 2 × 2 × 5

*(Note: You could also do 20 = 2 × 10, then 10 = 2 × 5 → same result)*

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Problem 8: 28

Tree shows 28 splits into ? and ?. Let’s use 4 × 7 = 28
Break 4 into 2 × 2
So: 28 = 2 × 2 × 7
Answer line: 28 = _ × _ × _ → 2 × 2 × 7

*(Alternatively: 28 = 2 × 14 → 14 = 2 × 7 → same answer)*

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Problem 9: 45

Tree shows 45 splits into ? and ?. Try 5 × 9 = 45
Break 9 into 3 × 3
So: 45 = 5 × 3 × 3 → or written as 3 × 3 × 5
Answer line: 45 = _ × _ × _ → 3 × 3 × 5

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✔ All problems solved! Now let’s write the final answers clearly for each problem.

Final Answer:
1) 35 = 5 × 7
2) 14 = 2 × 7
3) 33 = 3 × 11
4) 12 = 2 × 2 × 3
5) 30 = 2 × 3 × 5
6) 27 = 3 × 3 × 3
7) 20 = 2 × 2 × 5
8) 28 = 2 × 2 × 7
9) 45 = 3 × 3 × 5