Let’s solve each factor tree step by step. The goal is to break down each number into its
prime factors (numbers divisible only by 1 and themselves) and write the prime factor product.
---
Problem 1:
We are given:
- Top box is empty.
- It splits into
3 and
15.
- Then
15 splits into two empty circles.
Step 1: Find the top number.
Since 3 × 15 =
45, the top box is
45.
Step 2: Factor 15.
15 = 3 × 5 → both are prime.
✔ So, the completed tree:
- Top:
45
- Left branch:
3
- Right branch:
15 → which breaks into
3 and
5
Prime factor product:
>
45 = 3 × 3 × 5
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Problem 2:
Given:
- Top box is empty.
- Splits into
2 and an empty box.
- That empty box splits into
5 and
7.
Step 1: Find the middle box.
5 × 7 =
35
Step 2: Find the top number.
2 × 35 =
70
✔ Completed tree:
- Top:
70
- Left:
2
- Right:
35 → which breaks into
5 and
7
Prime factor product:
>
70 = 2 × 5 × 7
---
Problem 3:
Given:
- Top box is empty.
- Splits into two boxes.
- Left box splits into
5 and
3 → so that box is 5×3 =
15
- Right box splits into
2 and
3 → so that box is 2×3 =
6
Step 1: Top number = 15 × 6 =
90
✔ Completed tree:
- Top:
90
- Left branch:
15 → 5 and 3
- Right branch:
6 → 2 and 3
Prime factor product:
>
90 = 5 × 3 × 2 × 3
(We can reorder for clarity:
2 × 3 × 3 × 5)
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Problem 4:
Given:
- Top box:
126
- Splits into a circle and a box.
- The box splits into
3 and
14
-
14 splits into two empty circles.
Step 1: Find what goes with 3 and 14.
Since 3 × 14 = 42, the box next to 126 must be
42.
Then, 126 = ? × 42 → 126 ÷ 42 =
3
Wait — that would mean 126 = 3 × 42, but we already have 3 as a factor of 42. Let’s check:
Actually, looking at the structure:
Top: 126
→ splits into [circle] and [box labeled "3" and "14"]
So 126 = (unknown circle) × (3 × 14)
But 3 × 14 = 42 → so unknown circle = 126 ÷ 42 =
3
That means 126 =
3 × 42
But 42 = 3 × 14 → so 126 = 3 × 3 × 14
Now factor
14: 14 = 2 × 7
✔ So final prime factors:
3 × 3 × 2 × 7
Completed tree:
- Top:
126
- Left:
3
- Right:
42 → which splits into
3 and
14
-
14 splits into
2 and
7
Prime factor product:
>
126 = 3 × 3 × 2 × 7
(or ordered:
2 × 3 × 3 × 7)
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##
✔ Final Answers:
1)
45 = 3 × 3 × 5
2)
70 = 2 × 5 × 7
3)
90 = 2 × 3 × 3 × 5
4)
126 = 2 × 3 × 3 × 7
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You can now fill in all the blanks on the worksheet using these answers!
Parent Tip: Review the logic above to help your child master the concept of factor trees worksheets.
