Question

Determine the prime factorization of 88.

A.
2^2• 3 • 5

B.
2^3• 11

C.
2^2• 11

D.
2 • 3^2• 5

Answer 1

prime numbers are those whose only factors are 1 and the number. The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

prime factorization means finding the list of prime numbers which when multiplied together give you the number you are factoring. For example, the prime factorization of 10 is 2*5.

You can find the prime factorization by dividing the number by each successive prime as many times as it is divisible, then moving on to the next prime. 88 is divisible by 2, so there is at least one power of 2 in the prime factorization. Divide 88 by 2 repeatedly until you get a number that is no longer divisible by 2. At that point, try 3, then 5, then 7, then 11, etc. up until you have divided 88 down to 1.

I'll do 66 as an example:

66 is even, so it can be divided by 2. 66/2 = 33, which is no longer even, so we stop trying to divide by 2. 33/3 = 11. 11 is not divisible by 3, so we try 5, and then 7, but neither 5 nor 7 evenly divides 11. The next number on our list is 11, and 11 is divisible by 11, of course, so we are done, and our prime factorization of 66 is 2 * 3 * 11.