Question
The number 100 expressed as a product of its prime factors is Responses 4 × 52 4 × 52 - no response given 22 × 25 22 × 25 - no response given 22 × 52 22 × 52 - no response given 102
Answers
Answered by
GPT-4o mini
To express the number 100 as a product of its prime factors, we can start by finding its prime factorization.
1. First, divide 100 by the smallest prime number, which is 2:
\[
100 \div 2 = 50
\]
2. Continue factoring 50:
\[
50 \div 2 = 25
\]
3. Next, 25 is not divisible by 2, so we'll try the next prime number, which is 3. Since 25 is not divisible by 3, we try the next prime number, which is 5:
\[
25 \div 5 = 5
\]
4. Finally, 5 can be divided by itself:
\[
5 \div 5 = 1
\]
So the complete factorization is:
\[
100 = 2^2 \times 5^2
\]
Thus, the prime factorization of 100 in terms of powers of its prime factors is:
\[
100 = 2^2 \times 5^2
\]
From the given responses, the correct expression for the prime factorization of 100 is:
\[
2^2 \times 5^2
\]
1. First, divide 100 by the smallest prime number, which is 2:
\[
100 \div 2 = 50
\]
2. Continue factoring 50:
\[
50 \div 2 = 25
\]
3. Next, 25 is not divisible by 2, so we'll try the next prime number, which is 3. Since 25 is not divisible by 3, we try the next prime number, which is 5:
\[
25 \div 5 = 5
\]
4. Finally, 5 can be divided by itself:
\[
5 \div 5 = 1
\]
So the complete factorization is:
\[
100 = 2^2 \times 5^2
\]
Thus, the prime factorization of 100 in terms of powers of its prime factors is:
\[
100 = 2^2 \times 5^2
\]
From the given responses, the correct expression for the prime factorization of 100 is:
\[
2^2 \times 5^2
\]