Without dividing, determine if $91$ , $626$ is divisible by $6$ and explain how you know. $\newline$ $91,626 \square \text { divisible by } 6$

Full solution

Q. Without dividing, determine if

91

626

is divisible by

6

and explain how you know.

\newline

91,626 \square \text { divisible by } 6

Check Even Number: To determine if a number is divisible by $6$ , it must be divisible by both $2$ and $3$ . For a number to be divisible by $2$ , it must be even, which means its last digit must be $0$ , $2$ , $4$ , $6$ , or $8$ . Let's check if $91,626$ is even.
Add Digits: The last digit of $91,626$ is $6$ , which is an even number. Therefore, $91,626$ is divisible by $2$ .
Check Divisibility by $3$ : Next, to check if a number is divisible by $3$ , we add up all the digits in the number and see if the sum is divisible by $3$ . Let's add up the digits of $91,626$ : $9 + 1 + 6 + 2 + 6$ .
Calculate Sum: The sum of the digits is $9 + 1 + 6 + 2 + 6 = 24$ . Now we need to determine if $24$ is divisible by $3$ .
Divisibility by $3$ : Since $24$ is divisible by $3$ (as $24 \div 3 = 8$ ), the sum of the digits of $91,626$ is divisible by $3$ . Therefore, $91,626$ is divisible by $3$ .
Conclusion: Since $91,626$ is divisible by both $2$ and $3$ , we can conclude that $91,626$ is divisible by $6$ .