Prime factor trees worksheet for Grade 5 students to practice finding prime factors of numbers.

I'll solve this prime factor tree worksheet step by step.

First, let me understand what prime factor trees are. A prime factor tree is a diagram used to find the prime factors of a number. We start with the original number at the top, then break it down into two factors (usually starting with the smallest prime factor), and continue breaking down each non-prime factor until all branches end in prime numbers.

Let me work through each of the four problems:

Problem 1: Factor tree for 30
- 30 = 5 × 6 (since 5 is given as one factor)
- 6 = 2 × 3 (both 2 and 3 are prime)
- So the prime factors of 30 are 2, 3, and 5

Problem 2: Factor tree for 81
- 81 = 9 × 9 (since 9 is given as one factor)
- 9 = 3 × 3 (both 3s are prime)
- So the prime factors of 81 are 3, 3, 3, and 3 (or 3⁴)

Problem 3: Factor tree for 56
- 56 = 7 × 8 (we can choose 7 as one factor since it's prime)
- 8 = 2 × 4
- 4 = 2 × 2
- So the prime factors of 56 are 2, 2, 2, and 7 (or 2³ × 7)

Problem 4: Factor tree for 72
- 72 = 8 × 9 (we can break it down this way)
- 8 = 2 × 4, and 4 = 2 × 2
- 9 = 3 × 3
- So the prime factors of 72 are 2, 2, 2, 3, and 3 (or 2³ × 3²)

Let me now fill in the blanks for each tree:

For 30: The missing box next to 5 should be 6, and below 6 should be 2 and 3.
For 81: The missing box next to 9 should be 9, and below each 9 should be 3 and 3.
For 56: The left circle should be 7, the right box should be 8, below 8 should be 2 and 4, and below 4 should be 2 and 2.
For 72: The two boxes below 72 should be 8 and 9, below 8 should be 2 and 4, below 4 should be 2 and 2, below 9 should be 3 and 3.

Wait, let me reconsider the 56 and 72 trees to make sure I'm following the structure correctly.

Actually, looking at the structure again:
For 56: The first split is 7 and 8, then 8 splits into 2 and 4, then 4 splits into 2 and 2.
For 72: The first split could be 8 and 9, then 8 splits into 2 and 4, 4 splits into 2 and 2, and 9 splits into 3 and 3.

This looks correct based on the structure shown in the image.

The completed prime factor trees would show:
- 30: 5, 6 → 2, 3
- 81: 9, 9 → 3, 3 for each 9
- 56: 7, 8 → 2, 4 → 2, 2
- 72: 8, 9 → 2, 4 → 2, 2 for the 8 branch; 3, 3 for the 9 branch

This completes the prime factor trees for all four numbers.