To solve the problem, we need to complete the factorization of the given numbers (45, 24, 36, and 40) into their prime factors. Let's go through each number step by step.
---
1. Factorization of 45
The number 45 is already partially factored as:
```
45
/ \
5 9
/ \
3 3
```
- The prime factors are: \( 5 \times 3 \times 3 \).
Thus, the complete factorization of 45 is:
\[
45 = 5 \times 3 \times 3
\]
---
2. Factorization of 24
The number 24 is partially factored as:
```
24
/ \
8 3
/ \
4 2
/ \
2 2
```
- The prime factors are: \( 3 \times 2 \times 2 \times 2 \).
Thus, the complete factorization of 24 is:
\[
24 = 3 \times 2 \times 2 \times 2
\]
---
3. Factorization of 36
The number 36 is partially factored as:
```
36
/ \
6 6
/ \ / \
2 3 2 3
```
- The prime factors are: \( 2 \times 3 \times 2 \times 3 \).
Thus, the complete factorization of 36 is:
\[
36 = 2 \times 3 \times 2 \times 3
\]
---
4. Factorization of 40
The number 40 is partially factored as:
```
40
/ \
5 8
/ \
4 2
/ \
2 2
```
- The prime factors are: \( 5 \times 2 \times 2 \times 2 \).
Thus, the complete factorization of 40 is:
\[
40 = 5 \times 2 \times 2 \times 2
\]
---
Final Answers
Putting it all together, the complete factorizations are:
\[
\boxed{
45 = 5 \times 3 \times 3, \quad
24 = 3 \times 2 \times 2 \times 2, \quad
36 = 2 \times 3 \times 2 \times 3, \quad
40 = 5 \times 2 \times 2 \times 2
}
\]
Parent Tip: Review the logic above to help your child master the concept of prime factorization worksheet 5th grade.
