"prime factoring" is simply dividing the number by the lowest prime, except 1, and then the next higher and so on.
in short, your starting point is 2, and divide it by 2 till you can't anymore.
then 3, if it's divisible by 3, same, till you can't.
then 5, do the same, then 7, then 11 and so on.
we don't use say hmm 4 because 4 is 2*2, and the division by 2 will have shown any factors of 4 anyway, we don't use 6 either, because 2*3 is 6, and the division of 2 and 3, will have shown any factors of 6 if any at all and so on.
now let's do this fellow,
well, is not divisible by 2 certainly, so we skip that one.
1+4+7 = 12, now 12 is divisible by 3, so 147 is therefore also divisible by 3.
