Grade 5 Prime Factor Trees Worksheet - Complete the factor trees to find the prime factors of each number.

To solve this problem, we need to complete each factor tree by breaking down the numbers into their prime factors. A prime factor is a number that can only be divided by 1 and itself (like 2, 3, 5, 7, 11, etc.).

Let’s go one tree at a time.

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Tree 1: Number 30

We start with 30. It’s already split into 5 and a blank box.

Since 5 × ? = 30 → the missing number is 6.

Now break down 6: 6 = 2 × 3 (both are prime).

So the tree becomes:
- 30 → 5 and 6
- 6 → 2 and 3

Final prime factors: 5, 2, 3

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Tree 2: Number 81

81 is split into a blank box and 9.

Since 9 × ? = 81 → the missing number is 9.

Now break down each 9:

9 = 3 × 3 (both prime)

So both branches from 9 will be 3 and 3.

Final prime factors: 3, 3, 3, 3

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Tree 3: Number 56

56 is split into a blank circle and a blank square.

Let’s pick an easy factor pair. 56 ÷ 8 = 7 → so let’s say left circle is 7, right square is 8.

Now break down 8: 8 = 2 × 4 → but 4 isn’t prime, so break 4 further: 4 = 2 × 2.

So:
- 56 → 7 and 8
- 8 → 2 and 4
- 4 → 2 and 2

Final prime factors: 7, 2, 2, 2

*(Note: You could also start with 56 = 2 × 28, then 28 = 4 × 7, etc.—but the tree structure guides us. Since the left branch is a circle (likely meant to be prime), 7 makes sense there.)*

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Tree 4: Number 72

72 is split into two blank squares.

Let’s choose 8 and 9 (since 8 × 9 = 72).

Break down 8: 8 = 2 × 4 → then 4 = 2 × 2 → so 8 → 2, 2, 2

Break down 9: 9 = 3 × 3

So:
- 72 → 8 and 9
- 8 → 2 and 4 → 4 → 2 and 2
- 9 → 3 and 3

Final prime factors: 2, 2, 2, 3, 3

*(Alternative: 72 = 6 × 12, but again, the tree structure suggests splitting into two parts first — 8 and 9 works well here.)*

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Now, let’s fill in all the blanks as they appear in the original trees:

Tree 1 (30):
- Top: 30
- Left child: 5 (given)
- Right child (square): 6
- Children of 6: 2 and 3 (both circles)

Tree 2 (81):
- Top: 81
- Left child (square): 9
- Right child: 9 (given)
- Children of left 9: 3 and 3
- Children of right 9: 3 and 3

Tree 3 (56):
- Top: 56
- Left child (circle): 7
- Right child (square): 8
- Children of 8: left circle = 2, right square = 4
- Children of 4: 2 and 2

Tree 4 (72):
- Top: 72
- Left child (square): 8
- Right child (square): 9
- Children of 8: 2 and 4
- Children of 4: 2 and 2
- Children of 9: 3 and 3

Wait — looking back at the original image description for Tree 4:

> 72
> / \
> □ □
> / \ / \
> ○ ○ ○ □
> / \
> ○ ○

Actually, the right branch of 72 has a square that splits into two circles — meaning that square must be a composite number that breaks into two primes. So if we put 9 on the right, it splits into 3 and 3 — perfect.

On the left, 8 splits into 2 and 4 — but 4 is not prime, so the next level should break 4 into 2 and 2. But in the diagram, the left side of 72 has a square that splits into two circles — which implies those two circles are the final prime factors. That means the square under 72 on the left must be a number that breaks into two primes directly — like 8 breaks into 2 and 4? No, 4 isn’t prime.

Wait — perhaps the left square under 72 is meant to be 6? 6 = 2 × 3 — both prime. Then the right square is 12? 12 = 3 × 4 → no, 4 not prime. Or 12 = 2 × 6 → still not done.

Alternatively, maybe 72 = 36 × 2? But 36 is big.

Let me re-express based on standard factor trees and the diagram structure.

Looking again at Tree 4:

The root is 72.

It splits into two squares.

Left square splits into two circles → so left square must be a product of two primes → e.g., 6 (2×3), or 10 (2×5), etc.

Right square splits into a circle and a square → so right square must be a product of a prime and a composite → e.g., 12 = 3 × 4, then 4 = 2×2.

That fits!

So:

72 = 6 × 12

Left square: 6 → splits into 2 and 3 (circles)

Right square: 12 → splits into 3 and 4 (circle and square)

Then 4 → splits into 2 and 2 (circles)

Perfect match to the diagram.

So:

- 72 → 6 and 12
- 6 → 2 and 3
- 12 → 3 and 4
- 4 → 2 and 2

Final prime factors: 2, 3, 3, 2, 2 → same as before, just different path.

This matches the diagram exactly.

So let’s finalize all trees with correct placements:

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Tree 1: 30

- 30 → 5 and 6
- 6 → 2 and 3

Blanks filled:
- Square under 30: 6
- Two circles under 6: 2 and 3

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Tree 2: 81

- 81 → 9 and 9
- Each 9 → 3 and 3

Blanks filled:
- Left square under 81: 9
- Four circles: all 3s

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Tree 3: 56

- 56 → 7 and 8
- 8 → 2 and 4
- 4 → 2 and 2

Blanks filled:
- Left circle: 7
- Right square: 8
- Circle under 8: 2
- Square under 8: 4
- Two circles under 4: 2 and 2

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Tree 4: 72

- 72 → 6 and 12
- 6 → 2 and 3
- 12 → 3 and 4
- 4 → 2 and 2

Blanks filled:
- Left square: 6
- Right square: 12
- Circles under 6: 2 and 3
- Circle under 12: 3
- Square under 12: 4
- Circles under 4: 2 and 2

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All calculations verified. Prime factorizations are correct.

Final Answer:
Tree 1: 6, 2, 3
Tree 2: 9, 3, 3, 3, 3
Tree 3: 7, 8, 2, 4, 2, 2
Tree 4: 6, 12, 2, 3, 3, 4, 2, 2