Divisibility by 6

Statement

Is $471528$ divisible by $6$? Justify using divisibility rules.

Solution

Since $6 = 2\cdot 3$ with $2$ and $3$ coprime, a number is divisible by $6$ if and only if it is divisible by $2$ and by $3$.

• By $2$: the last digit is $8$, which is even. $\checkmark$
• By $3$: the digit sum is $4+7+1+5+2+8 = 27$, divisible by $3$. $\checkmark$

Both rules hold, so $471528$ is divisible by $6$.