Is 101 a prime number?

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Answer 1 · 2016-04-07T23:16:50

Yes, it has no positive factors apart from #1# and #101#.

To test if #101# is prime, check for divisibility by each of the primes #2#, #3#, #5# and #7#.

There is no need to check beyond these as #11^2 = 121 > 101#.

So if #101# was divisible by some number less than #101# then it would be divisible by a number less than #11#.

#101# is not divisible by #2# since it ends with an odd digit.

#101# is not divisible by #3# since the sum of its digits is not divisible by #3#

#101# is not divisible by #5# since its last digit is neither #5# nor #0#.

#101# is not divisible by #7# since #101/7 = 14# with remainder #3#.