To find the prime factorization of 475, we start by dividing the number by the smallest prime number, which is 2. Since 475 is an odd number, it is not divisible by 2. The next prime number is 3, and we can check for divisibility by adding the digits of 475 (4 + 7 + 5 = 16), which is not divisible by 3. Next, we check 5, since 475 ends with a 5, it is divisible by 5.
So we divide:
475 ÷ 5 = 95
Now we need to factor 95. Again, we can start with 5, since 95 also ends with a 5:
95 ÷ 5 = 19
Now we have 19, which is a prime number. There are no factors other than 1 and 19 for this number. Therefore, we have reached the end of our factorization.
Putting it all together, the prime factorization of 475 is:
5 x 5 x 19 or, more compactly, 5² x 19.