Prime factorization is finding which prime numbers can be multiplied to get the number that they give you originally E.J. if they give you 24 and find 2 numbers that factor it the first that would come to mind would be 12 times 2 well 2 can't be simplified no more but 12 can, 12 can have factors of 3 and 4, now 3 cant be factored but 4 can, 4 can be multiplied by 2 times 2... so now that you factored it completely you know that 2*2*2*3=24. lets check it out 2 times 2 is 4 4 times 2 is 8 and 8 times 3 is 24. this means our factors are correct!!!
Hope this helps