Write the prime factorization of 175. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).Submit

The prime factorization of 175 is done by dividing the number by prime numbers. Here are the steps:

1. Start by dividing 175 by the smallest prime number, which is 2. Since 175 is not divisible by 2, we move to the next prime number, which is 3. It's also not divisible by 3.

2. The next prime number is 5. 175 divided by 5 is 35. So, 5 is a prime factor of 175.

3. Now, we divide 35 (the quotient we got from the last step) by the smallest prime number, which is 2. Since 35 is not divisible by 2, we move to the next prime number, which is 3. It's also not divisible by 3.

4. The next prime number is 5. 35 divided by 5 is 7. So, 5 is a prime factor of 175.

5. Now, we divide 7 (the quotient we got from the last step) by the smallest prime number, which is 2. Since 7 is not divisible by 2, we move to the next prime number, which is 3. It's also not divisible by 3.

6. The next prime number is 5. Since 7 is not divisible by 5, we move to the next prime number, which is 7. 7 divided by 7 is 1. So, 7 is a prime factor of 175.

7. Now, we have reached 1, and we can stop.

So, the prime factorization of 175 is 5^2 * 7. We use an exponent of 2 for 5 because 5 is a factor twice. The factors are already in order from least to greatest.