describe how you would find the prime factorization of 125?

Answer 1

125=25*5
25=5*5
125=5^3

Answer 2

Start at the beginning of the primes (2), and see if they divide evenly into 125. For example:

Does 2 divide into 125? No.
Does 3 divide into 125? No.
Does 5 divide into 125? Yes. 125/5 = 25, so you have:

5 x (25).

Then, you repeat the process for the number you have left.
Does 2 divide into 25? No.
Does 3 divide into 25? No.
Does 5 divide into 25? Yes. 25/5 = 5, so you have:

5 x 5, which you replace 25 with up above, to get 5 x 5 x 5.

So, for example, with 312. Keep on dividing by 2 until you can't any more. You get:

2 x 156
2 x (2 x 78)
2 x 2 x (2 x 39)

Now, because you can't divide by 2 any more, go to the next prime, 3, and start dividing by that.

2 x 2 x 2 x (3 x 13).

You should realize by now that these are all prime numbers, so your prime factorization of 312 is 2 x 2 x 2 x 3 x 13.

Answer 3

125 =
5 x 25

25 = 5 x 25

25 =5 x 5

Prime factorization = 5 x 5 x 5 x 5

Answer 4

Make life easy for yourself by noticing that the units digit is a 5, which means it's divisible by 5

125=5*25
ah ha! , now factor the 25:
125=5*5*5

Thus 125 is 5^3

Answer 5

125 divided by 5 =25
25 divided by 5=5
5 divided by 5=1

So, the prime factorization of 125=5*5*5

Answer 6

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RE:
describe how you would find the prime factorization of 125?

Answer 7

I like alokpinto's answer; I'd add that you can limit your search by taking the square root of the number; no prime larger than that can be a factor.

Answer 8

I would divide by 5 twice, yielding 5*5*5