Without dividing, determine if $79$ , $644$ is divisible by $3$ and explain how you know. $\newline$ $79,644 \square$ divisible by $3$

Full solution

Q. Without dividing, determine if

79

644

is divisible by

3

and explain how you know.

\newline

79,644 \square

divisible by

3

Divisibility Rule for $3$ : To determine if a number is divisible by $3$ , we can use the divisibility rule for $3$ : if the sum of the digits of the number is divisible by $3$ , then the number itself is divisible by $3$ . Let's apply this rule to $79,644$ .
Add Digits Together: First, we add the digits of $79,644$ together: $7 + 9 + 6 + 4 + 4$ .
Calculate Sum: The sum of the digits is $7 + 9 + 6 + 4 + 4 = 30$ .
Check Divisibility: Now, we check if the sum we found, which is $30$ , is divisible by $3$ . Since $30$ divided by $3$ equals $10$ , which is a whole number, $30$ is divisible by $3$ .
Conclusion: Because the sum of the digits of $79,644$ is divisible by $3$ , we can conclude that $79,644$ is also divisible by $3$ .