Answer:
Explanation:
To create a Venn diagram using the prime factors of the numbers 252, 270, and 300, we first need to find the prime factors of each number. Then, we can represent the common and unique prime factors in the Venn diagram. Here are the prime factorizations of these numbers:
1. Prime factors of 252:
- \(252 = 2^2 \cdot 3^2 \cdot 7\)
2. Prime factors of 270:
- \(270 = 2 \cdot 3^3 \cdot 5\)
3. Prime factors of 300:
- \(300 = 2^2 \cdot 3 \cdot 5^2\)
Now, let's create a Venn diagram to represent these prime factors:
```
2
/ \
/ \
252 270
/ \ /
/ \ /
2^2 3^2 2
\ \ / \
\ \/
7 3^3
/ \
5 5^2
```
In this Venn diagram:
- The number 2 is a common prime factor to all three numbers.
- The number 3 is a common prime factor to 252 and 270.
- The number 5 is a common prime factor to 270 and 300.
- The number 7 is a unique prime factor to 252.
- The number 5^2 and 3^3 are unique prime factors to 270.
- The number 2^2 is a unique prime factor to 252 and 300.
This Venn diagram visually represents the prime factors of the numbers 252, 270, and 300, showing their common and unique factors.