The image shows two
factor trees for the number
42, which is being broken down into its
prime factors. Let's analyze both trees and explain the solution.
---
🔍 Understanding Factor Trees
A
factor tree is a diagram used to break down a number into its
prime factors — that is, the prime numbers that multiply together to give the original number.
We'll go through each tree step by step.
---
🌲 Left Factor Tree:
```
42
/ \
6 7
/ \
2 3
```
- Start with
42
- Break it into
6 × 7
- Then break
6 into
2 × 3
-
7 is already a prime number
So the prime factors are:
2 × 3 × 7
✔ All are prime numbers → this is the
prime factorization of 42.
---
🌲 Right Factor Tree:
```
42
/ \
2 21
/ \
3 7
```
- Start with
42
- Break it into
2 × 21
- Then break
21 into
3 × 7
-
2,
3, and
7 are all prime
So the prime factors are:
2 × 3 × 7
✔ Again, same result!
---
✔ Conclusion:
Both factor trees correctly show the
prime factorization of
42.
>
Prime factorization of 42 = 2 × 3 × 7
Even though the
path to get there is different (one starts with 6×7, the other with 2×21), both lead to the
same set of prime factors.
This demonstrates that
prime factorization is unique (Fundamental Theorem of Arithmetic) — no matter how you split the number, you end up with the same primes.
---
🎯 Final Answer:
$$
\boxed{2 \times 3 \times 7}
$$
This is the
prime factorization of 42, confirmed by both factor trees.
Parent Tip: Review the logic above to help your child master the concept of lcm factor tree worksheet.
