Question
Write 100 as a product of prime factors. \( 100= \) II
Ask by Nichols Moreno. in the United States
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(100 = 2^2 \times 5^2\).
Solution
1. Begin with the number \(100\).
2. Divide by the smallest prime \(2\):
\[
100 \div 2 = 50.
\]
3. Divide \(50\) by \(2\) again:
\[
50 \div 2 = 25.
\]
4. Now, \(25\) is not divisible by \(2\); try the next prime number \(5\):
\[
25 \div 5 = 5.
\]
5. Divide \(5\) by \(5\):
\[
5 \div 5 = 1.
\]
6. Since we reached \(1\), the factorization is complete. The prime factors used are \(2\) and \(5\).
7. Write the prime factorization in exponential form:
\[
100 = 2^2 \times 5^2.
\]
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Simplify this solution Beyond the Answer
100 can be broken down into prime factors starting with its smallest prime, which is 2. Dividing 100 by 2 gives us 50, and dividing 50 by 2 again gives us 25. Now, since 25 isn't divisible by 2, we switch to the next prime, which is 5. Dividing 25 by 5 gives us 5, and dividing 5 by 5 gives us 1. Therefore, we can write 100 as: \( 100 = 2^2 \times 5^2 \)
