Prime factor trees worksheet for practicing factorization of numbers.

To solve these prime factor trees, we need to break each number down into its prime factors. A prime factor is a number that can only be divided by 1 and itself (like 2, 3, 5, 7, 11...).

Here is the step-by-step solution for each tree:

1. Number 18
* The tree starts with 18 splitting into 2 and a blank box.
* $18 \div 2 = 9$. So, the blank box is 9.
* Now we look at the branches coming from 9. They are 3 and a blank circle.
* $9 \div 3 = 3$. So, the blank circle is 3.
* *Check:* $2 \times 3 \times 3 = 18$. Correct.

2. Number 27
* The tree starts with 27 splitting into a blank circle and 9.
* $27 \div 9 = 3$. So, the first blank circle is 3.
* Now we look at the branches coming from 9. It splits into two blank circles.
* We know that $3 \times 3 = 9$. So, both bottom circles are 3.
* *Check:* $3 \times 3 \times 3 = 27$. Correct.

3. Number 20
* The tree starts with 20 splitting into 2 and a blank box.
* $20 \div 2 = 10$. So, the blank box is 10.
* Now we look at the branches coming from 10. It splits into two blank circles.
* We need two numbers that multiply to make 10. Since we want prime numbers, we use 2 and 5 ($2 \times 5 = 10$).
* *Check:* $2 \times 2 \times 5 = 20$. Correct.

4. Number 42
* The tree starts with 42 splitting into 2 and a blank box.
* $42 \div 2 = 21$. So, the blank box is 21.
* Now we look at the branches coming from 21. It splits into two blank circles.
* We need two prime numbers that multiply to make 21. Those are 3 and 7 ($3 \times 7 = 21$).
* *Check:* $2 \times 3 \times 7 = 42$. Correct.

5. Number 52
* The tree starts with 52 splitting into 2 and a blank box.
* $52 \div 2 = 26$. So, the blank box is 26.
* Now we look at the branches coming from 26. It splits into two blank circles.
* We need two prime numbers that multiply to make 26. Those are 2 and 13 ($2 \times 13 = 26$).
* *Check:* $2 \times 2 \times 13 = 52$. Correct.

6. Number 30
* The tree starts with 30 splitting into 2 and a blank box.
* $30 \div 2 = 15$. So, the blank box is 15.
* Now we look at the branches coming from 15. It splits into two blank circles.
* We need two prime numbers that multiply to make 15. Those are 3 and 5 ($3 \times 5 = 15$).
* *Check:* $2 \times 3 \times 5 = 30$. Correct.

Final Answer:
18: Box: 9, Circle: 3
27: Left Circle: 3, Bottom Circles: 3 and 3
20: Box: 10, Bottom Circles: 2 and 5
42: Box: 21, Bottom Circles: 3 and 7
52: Box: 26, Bottom Circles: 2 and 13
30: Box: 15, Bottom Circles: 3 and 5