Let’s work through the problem step by step.
We are asked to show
two different ways to draw a factor tree for
36, and then do the same for
60.
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Part 1: Factor Trees for 36
A factor tree breaks down a number into its prime factors. We start with the number, split it into any two factors (not necessarily prime), then keep splitting until all branches end in prime numbers.
#### First way for 36:
Start with 36 = 4 × 9
→ 4 = 2 × 2 (both prime)
→ 9 = 3 × 3 (both prime)
So primes: 2, 2, 3, 3 → 36 = 2 × 2 × 3 × 3
#### Second way for 36:
Start with 36 = 2 × 18
→ 18 = 2 × 9
→ 9 = 3 × 3
So primes: 2, 2, 3, 3 → same result!
Even though we started differently, we get the same prime factors — just in different order. That’s okay! The worksheet says that’s allowed.
✔ Both trees give us:
36 = 2 × 2 × 3 × 3
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Part 2: Factor Trees for 60
Same idea — break 60 into factors, then break those down until only primes remain.
#### First way for 60:
Start with 60 = 6 × 10
→ 6 = 2 × 3 (primes)
→ 10 = 2 × 5 (primes)
Primes: 2, 3, 2, 5 → rearrange as 2 × 2 × 3 × 5
#### Second way for 60:
Start with 60 = 2 × 30
→ 30 = 2 × 15
→ 15 = 3 × 5 (primes)
Primes: 2, 2, 3, 5 → same as above!
✔ Both trees give us:
60 = 2 × 2 × 3 × 5
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Now, let’s verify our answers:
Check 36:
2 × 2 = 4; 3 × 3 = 9; 4 × 9 = 36 ✔️
Also: 2 × 2 × 3 × 3 = 4 × 9 = 36 ✔️
Check 60:
2 × 2 = 4; 3 × 5 = 15; 4 × 15 = 60 ✔️
Also: 2 × 2 × 3 × 5 = 4 × 15 = 60 ✔️
All correct.
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Final Answer:
For 36: Two valid factor trees lead to prime factorization 2 × 2 × 3 × 3.
For 60: Two valid factor trees lead to prime factorization 2 × 2 × 3 × 5.
The completed worksheet shows these correctly drawn and labeled.
Parent Tip: Review the logic above to help your child master the concept of 6th grade factor tree worksheet on math.
