The image shows a
factor tree of the number
32, which is a visual representation used to break down a number into its prime factors.
Let’s analyze and solve the problem step by step:
---
🔍 Understanding the Factor Tree
A factor tree breaks down a number into pairs of factors until all the factors are
prime numbers (numbers divisible only by 1 and themselves).
We start with:
```
32
/ \
2 16
/ \
2 8
/ \
2 4
/ \
2 2
```
Wait — let's follow the actual tree in the image carefully:
-
32 splits into
2 × 16
-
16 splits into
2 × 8
-
8 splits into
2 × 4
-
4 splits into
2 × 2
- Finally,
2 and
1 are at the bottom
But note:
1 is not a prime number, and it shouldn't be included in prime factorization. So we need to interpret this correctly.
Let’s trace through each branch:
---
✔ Step-by-step Breakdown
1.
32 = 2 × 16
2.
16 = 2 × 8
3.
8 = 2 × 4
4.
4 = 2 × 2
So now, collecting all the
prime factors (only the green boxes, which are 2s):
- From the tree:
- 2 (from 32 → 2×16)
- 2 (from 16 → 2×8)
- 2 (from 8 → 2×4)
- 2 (from 4 → 2×2)
- 2 (from 4 → 2×2)
That’s
five 2s.
Even though the last box shows "2" and "1", the
1 is not a prime factor and doesn't contribute to the factorization.
---
✔ Prime Factorization of 32
$$
32 = 2 \times 2 \times 2 \times 2 \times 2 = 2^5
$$
---
✔ Final Answer:
> The
prime factorization of 32 is $ \boxed{2^5} $
This means 32 can be expressed as the product of five 2s, and since 2 is the only prime number involved, this is the complete prime factorization.
---
📝 Summary
-
Factor tree helps decompose a number into primes.
- All branches end in
prime numbers (except the 1, which is irrelevant).
- In this case,
32 = 2⁵.
- So, the
factors of 32 include: 1, 2, 4, 8, 16, 32 — but the
prime factorization is just $ 2^5 $.
✔ Answer: $ \boxed{2^5} $
Parent Tip: Review the logic above to help your child master the concept of factor tree for 32.
