Using divisibility tests, determine the given number $78,651$ is divisible by $6$.

Divisibility by 6:

We know that A number is divisible by $6$, if it is divisible by both $2$ and $3$.

Here, the given number is $78,651$. Since, ending digit is $1$, it will not be divisible by $2$ and the Sum of the digits of the given number is $7+8+6+5+1=27$ which is a multiple of $3$, so it will be divisible by $3$.

Since, the given number is divisible by $3$ only.

Therefore, the given number will not be divisible by $6$.