Without dividing, determine if $34$ , $757$ is divisible by $9$ and explain how you know. $\newline$ $34,757 \square$ divisible by $9$

Full solution

Q. Without dividing, determine if

34

757

is divisible by

9

and explain how you know.

\newline

34,757 \square

divisible by

9

Divisibility Rule for $9$ : To determine if a number is divisible by $9$ , we can use the divisibility rule for $9$ , which states that a number is divisible by $9$ if the sum of its digits is divisible by $9$ .
Add Digits of Number: First, we add the digits of the number $34,757$ : $3 + 4 + 7 + 5 + 7$ .
Calculate Sum: Performing the addition, we get $3 + 4 + 7 + 5 + 7 = 26$ .
Check Divisibility: Now, we need to check if the sum of the digits, which is $26$ , is divisible by $9$ . Since $26$ is not divisible by $9$ (because $9 \times 2 = 18$ and $9 \times 3 = 27$ , and $26$ is between these two products), we can conclude that the original number, $34,757$ , is not divisible by $9$ .