Question

Which of the following represents the prime factorization of 75?

0 3²x5
O 3*52
0 2x52
2*3*5

Answer 1

The prime factorization of 75 is obtained by dividing the number by the smallest prime factors, resulting in 3 x 5^2. This indicates that the number 75 is made up of one 3 and two fives.

Step-by-step explanation:

The prime factorization of a number is breaking down that number into the product of its prime factors. For the number 75, let's identify its prime factors:

1. Start by dividing 75 by the smallest prime number possible, which is 2. Since 75 is odd, it's not divisible by 2.
2. Move to the next prime number, which is 3. 75 divided by 3 gives 25, so we have one factor of 3.
3. The quotient we got is 25, which is 5 squared (52). So, the other factors are two 5s.

Putting it all together, the prime factorization of 75 is 3 x 52.

This means the correct answer from the given options is 3 x 52, as the number 75 is composed of one 3 and two 5s.