Question

write the prime factorization of 175. use exponents when appropriate and order the factors from least to greatest (for example, $2^2 \cdot 3 \cdot 5$).

Explanation:

Step1: Divide by smallest prime

Start with the smallest prime factor of 175, which is 5. \( 175 \div 5 = 35 \).

Step2: Divide again by 5

Now, factorize 35. Again, divide by 5: \( 35 \div 5 = 7 \).

Step3: Check prime factor

7 is a prime number, so we stop here.

Step4: Write prime factorization

The prime factors of 175 are 5, 5, and 7. Using exponents, this is \( 5^2 \cdot 7 \).

Answer:

\( 5^2 \cdot 7 \)