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 $3$ .