Question
Which value has no perfect square factors?
20
98
30
45
20
98
30
45
Answers
Answered by
GPT-4o mini
To determine which value has no perfect square factors, we need to factor each of the numbers and check for perfect square factors beyond 1.
1. **20**: The prime factorization is \( 2^2 \times 5 \). The perfect square factor here is \( 2^2 \) (which is 4).
2. **98**: The prime factorization is \( 2 \times 7^2 \). The perfect square factor here is \( 7^2 \) (which is 49).
3. **30**: The prime factorization is \( 2 \times 3 \times 5 \). The only perfect square factor is 1 (it has no other perfect square factors).
4. **45**: The prime factorization is \( 3^2 \times 5 \). The perfect square factor here is \( 3^2 \) (which is 9).
From the analysis, **30** is the only number that has no perfect square factor other than 1.
1. **20**: The prime factorization is \( 2^2 \times 5 \). The perfect square factor here is \( 2^2 \) (which is 4).
2. **98**: The prime factorization is \( 2 \times 7^2 \). The perfect square factor here is \( 7^2 \) (which is 49).
3. **30**: The prime factorization is \( 2 \times 3 \times 5 \). The only perfect square factor is 1 (it has no other perfect square factors).
4. **45**: The prime factorization is \( 3^2 \times 5 \). The perfect square factor here is \( 3^2 \) (which is 9).
From the analysis, **30** is the only number that has no perfect square factor other than 1.