Find the prime factorization of the composite number.
\[
175
\]
\[
175=
\]

Step 1 ：First, we need to find the prime factors of 175. We start by dividing 175 by the smallest prime number, which is 2. Since 175 is not divisible by 2, we try the next prime number, which is 3. Again, 175 is not divisible by 3. We continue this process until we find a prime number that can divide 175. The next prime number, 5, can divide 175. So, we divide 175 by 5 to get 35.

Step 2 ：We repeat the process for 35. It is not divisible by 2 or 3, but it is divisible by 5. So, we divide 35 by 5 to get 7.

Step 3 ：Finally, we check 7. Since 7 is a prime number, we have found all the prime factors of 175.

Step 4 ：Therefore, the prime factorization of 175 is \(5^2\cdot7^1\).

Step 5 ：So, \(175=5^2\cdot7^1\).

Step 6 ：\(\boxed{175=5^2\cdot7^1}\)