Is 247 prime?

Statement

Is $247$ prime? If not, give a factorization.

Solution

It is enough to test the primes up to $\sqrt{247}\approx 15.7$, namely $2,3,5,7,11,13$.

• Not even, so not divisible by $2$.
• $2+4+7=13$ is not a multiple of $3$.
• It does not end in $0$ or $5$: not divisible by $5$.
• $247 = 7\cdot 35 + 2$: not divisible by $7$.
• $247 = 11\cdot 22 + 5$: not divisible by $11$.
• $247 = 13\cdot 19$: divisible by $13$!

Hence $247$ is not prime: $247 = \boxed{13\cdot 19}$.