Which is the prime factorization of 86?

1 Answer
George C.
Feb 9, 2017

#86=2xx43#

Explanation:

First note that #86# ends with an even digit #6# so is itself divisible by #2#:

#86 = 2 xx 43#

You may know that #43# is prime, but let's verify:

  • #43# ends with an odd digit, so is not divisible by #2#

  • The sum of the digits of #43# is #4+3 = 7#, which is not divisible by #3#, so #43# is not divisible by #3# either.

  • The last digit of #43# is not #0# or #5#, so it is not divisible by #5#.

  • #43/7 = 6# with remainder #1#

Note that #7^2 = 49 > 43#, so there can be no other prime factors greater than #7# without there being one less than #7# too.

So #43# is prime.

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