How do you find the prime factorization on 75?

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Answer 1 · 2017-01-11T00:55:07

Divide by prime factors to find that

#75 = 3xx5xx5 = 3xx5^2#

The simplest way of finding the prime factorization of an integer is to divide by prime factors until the result is a prime.

First, we can see that #75# is divisible by #5#, as it ends in #5#. Dividing, we get

#75 -: color(red)(5) = 15#

Next, #15# is also divisible by #5#, so we divide again.

#15 -: color(red)(5) = 3#

Finally, #3# is a prime number, so it, together with the divisors in the prior steps, form the prime factorization of #75#.

#75 = 3xx5xx5#

Answer 2 · 2017-01-11T00:55:07

Keep on trying to divide by the primes in succession:

2 doesn't go into 75
3 does: #75=3xx25#
another 3 doesn't go into 25
5 does: #75=3xx5xx5#

And there it ends, because the last #5# is also prime.