Factor Tree Worksheet for Prime Factorization Practice

Let’s solve each factor tree step by step. We’ll break down each number into its prime factors — that means only numbers divisible by 1 and themselves (like 2, 3, 5, 7, etc.).

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First Tree: 54

Start with 54.

- 54 ÷ 2 = 27 → so one branch is 2, other is 27
- 27 ÷ 3 = 9 → so 27 breaks into 3 and 9
- 9 ÷ 3 = 3 → so 9 breaks into 3 and 3

So the full breakdown:
54 → 2 × 27 → 2 × 3 × 9 → 2 × 3 × 3 × 3

Prime factors: 2, 3, 3, 3

Apples at bottom should be filled with: 2, 3, 3, 3

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Second Tree: 81

Start with 81.

- 81 ÷ 3 = 27 → branches: 3 and 27
- 27 ÷ 3 = 9 → branches: 3 and 9
- 9 ÷ 3 = 3 → branches: 3 and 3

Full breakdown:
81 → 3 × 27 → 3 × 3 × 9 → 3 × 3 × 3 × 3

Prime factors: 3, 3, 3, 3

Apples: 3, 3, 3, 3

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Third Tree: 72

Start with 72.

- 72 ÷ 2 = 36 → branches: 2 and 36
- 36 2 = 18 → branches: 2 and 18
- 18 ÷ 2 = 9 → branches: 2 and 9
- 9 ÷ 3 = 3 → branches: 3 and 3

Wait — let’s check if we can do it more efficiently or correctly based on tree structure.

Looking at the tree shape for 72:

Top: 72 splits into two boxes.

Then one of those splits again, then another split... ending in 5 apples? Wait — no, looking back at image description: under 72 there are 5 apples? Actually, from original problem layout:

Actually, rechecking: In the worksheet, under 72 there are 5 apples? But 72 has only 4 prime factors: 2×2×2×3×3? Wait — 72 = 8 × 9 = 2³ × 3² → that’s 5 prime factors: 2,2,2,3,3

Yes! So:

72 → 2 × 36
36 → 2 × 18
18 → 2 × 9
9 → 3 × 3

So path: 72 → 2, 36 → 2, 18 → 2, 9 → 3, 3

Thus prime factors: 2, 2, 2, 3, 3

Apples: 2, 2, 2, 3, 3

But wait — the tree might not follow this exact branching order. Let’s match the visual structure described.

From user’s image description: For 72, the tree has:

- Top: 72
- Splits into two boxes (left and right)
- Left box stays as is? Or splits? Actually, according to standard factor trees and the example given (100 → 2 and 50; 50→2 and 25; 25→5 and 5), we always split until primes.

Assuming the tree for 72 is structured like:

72
├─ ?
└─ ?

Then one of them splits further, etc., until all leaves are primes.

Since 72 = 2 × 2 × 2 × 3 × 3, regardless of branching order, the final prime factors are five numbers: three 2s and two 3s.

Same for others.

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Fourth Tree: 450

Start with 450.

Break it down:

450 2 = 225 → so 2 and 225
225 ÷ 3 = 75 → 3 and 75
75 ÷ 3 = 25 → 3 and 25
25 ÷ 5 = 5 → 5 and 5

So: 450 → 2 × 225 → 2 × 3 × 75 → 2 × 3 × 3 × 25 → 2 × 3 × 3 × 5 × 5

Prime factors: 2, 3, 3, 5, 5

That’s 5 prime factors → matches 5 apples under 450.

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Now, fill in the blanks inside the trees (the white boxes) as well as the apples.

But the question says: “Fill in the apple blanks with their prime factors.” And also asks: “What are the factors inside the apples?”

So probably, we just need to list the prime factors that go in the apples at the bottom of each tree.

Also, note: in the example, 100 → factors were 2,2,5,5 → shown in 4 apples.

So for each number, list the prime factors in the apples.

Let’s summarize:

✔ 54: Prime factors = 2, 3, 3, 3 → Apples: [2, 3, 3, 3]

✔ 81: Prime factors = 3, 3, 3, 3 → Apples: [3, 3, 3, 3]

✔ 72: Prime factors = 2, 2, 2, 3, 3 → Apples: [2, 2, 2, 3, 3]

✔ 450: Prime factors = 2, 3, 3, 5, 5 → Apples: [2, 3, 3, 5, 5]

We don’t need to fill the internal boxes unless asked — but the main instruction is to fill the *apple blanks* with prime factors.

The squirrel asks: “What are the factors inside the apples?” — meaning, what numbers go in the red apples at the bottom.

So final answer should list the prime factors for each number, corresponding to the apples under each tree.

Order may matter depending on how the tree branches, but since multiplication is commutative, any order is fine — though typically we write smallest first.

In the example, they wrote: 2, 2, 5, 5 — sorted.

So we’ll sort them.

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Double-check calculations:

54:
54 ÷ 2 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 3 = 1 → primes: 2,3,3,3 ✔️

81:
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 3 = 1 → primes: 3,3,3,3 ✔️

72:
72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1 → primes: 2,2,2,3,3 ✔️

450:
450 2 = 225
225 ÷ 3 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1 → primes: 2,3,3,5,5 ✔️

All correct.

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Final Answer:
For 54: 2, 3, 3, 3
For 81: 3, 3, 3, 3
For 72: 2, 2, 2, 3, 3
For 450: 2, 3, 3, 5, 5