What would the prime factorization of 3500 be?

One way (not nessarily the easiest):

Divide by 2: 3500 / 2 = 1750

Divide by 2: 1750 / 2 = 875            

(875 can't be evenly divided by 2 again; so try the next prime number: 3.

Since 875 can't be evenly divided by 3, try 5.) 

Divide by 5: 875 / 5 = 175

Divide by 5: 175 / 5 = 35

Divide by 5: 35 / 5 = 7

(Since 7 is a prime number, quit. It is the last factor)

Multiply all those you divided by: 2 x 2 x 5 x 5 x 5 x 7 

So, the prime factorization of 3500 is 2 x 2 x 5 x 5 x 5 x 7