What is the prime factorization of 82?

1 Answer
Mar 30, 2017

#82 = color(green)(2 xx 41)#

Explanation:

Starting with the smallest prime, #2#
#82 = 2 xx 41#

#41# is not divisible by #2#, so try the next smallest prime #3#

...but #41# is not divisible by #3#, so try the next smallest prime #5#

...but #41# is not divisible by #5#, so try the next smallest prime #7#

...but #41# is not divisible by #7#
#color(white)("XXX")#and there is no need to check any further since
#color(white)("XXX")#if #41# were divisible by something bigger than #7#
#color(white)("XXX")#then it would need a factor smaller than #7#
#color(white)("XXX")#and we have ruled out all such possibilities.

i.e. #41# is prime

and the prime factors of #82# can not be reduced further than #2xx41#