Prime factor trees worksheet for Grade 5 students to find prime factors of given numbers.

I'll solve this prime factor tree worksheet by completing each tree to find the prime factors of the given numbers. Let me work through each one systematically.

First, let's look at the tree for 30:

- We're given that 30 = 5 × ?
- Since 30 ÷ 5 = 6, the missing number is 6
- Now we need to break down 6 into its prime factors: 6 = 2 × 3
- Both 2 and 3 are prime numbers

Next, the tree for 81:

- We're given that 81 = ? × 9
- Since 81 ÷ 9 = 9, the missing number is 9
- Now we need to break down both 9s: 9 = 3 × 3
- So 81 = 9 × 9 = (3 × 3) × (3 × 3) = 3⁴

Now, the tree for 56:

- We need to find two factors of 56
- One obvious pair is 7 × 8 (since 7 × 8 = 56)
- 7 is already prime
- 8 can be broken down as 2 × 4, and then 4 = 2 × 2
- So 56 = 7 × 2 × 2 × 2 = 7 × 2³

Finally, the tree for 72:

- We need to find two factors of 72
- One possible pair is 8 × 9 (since 8 × 9 = 72)
- 8 = 2 × 4 = 2 × 2 × 2 = 2³
- 9 = 3 × 3 = 3²
- So 72 = 2³ × 3²

Let me verify my answers by filling in the trees:

For 30:
- Top: 30
- Branches: 5 and 6
- 6 branches into: 2 and 3
- Prime factors: 2, 3, 5

For 81:
- Top: 81
- Branches: 9 and 9
- Each 9 branches into: 3 and 3
- Prime factors: 3, 3, 3, 3 (or 3⁴)

For 56:
- Top: 56
- Branches: 7 and 8
- 8 branches into: 2 and 4
- 4 branches into: 2 and 2
- Prime factors: 2, 2, 2, 7 (or 2³ × 7)

For 72:
- Top: 72
- Branches: 8 and 9
- 8 branches into: 2 and 4, then 4 into 2 and 2
- 9 branches into: 3 and 3
- Prime factors: 2, 2, 2, 3, 3 (or 2³ × 3²)

The completed prime factor trees show the prime factorization of each number.