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Without dividing, determine if 77,528 is divisible by 6 and explain how you know.

77,528◻ divisible by 6

Without dividing, determine if $77$ , $528$ is divisible by $6$ and explain how you know. $\newline$ $77,528 \square$ divisible by $6$

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Evaluate two-variable equations: word problems

Full solution

Q. Without dividing, determine if

77

,

528

is divisible by

6

and explain how you know.

\newline

77,528 \square

divisible by

6

Check Divisibility by $2$ : To determine if a number is divisible by $6$ , it must be divisible by both $2$ and $3$ . $\newline$ First, we check if the number is divisible by $2$ . A number is divisible by $2$ if its last digit is even ( $0, 2, 4, 6,$ or $8$ ). $\newline$ The last digit of $77,528$ is $8$ , which is even. $\newline$ Therefore, $77,528$ is divisible by $2$ .
Check Divisibility by $3$ : Next, we check if the number is divisible by $3$ . A number is divisible by $3$ if the sum of its digits is divisible by $3$ . $\newline$ The sum of the digits of $77,528$ is $7 + 7 + 5 + 2 + 8 = 29$ .
Sum of Digits: The sum $29$ is not divisible by $3$ because $3$ does not divide evenly into $29$ . Therefore, $77,528$ is not divisible by $3$ .
Final Divisibility Conclusion: Since $77,528$ is divisible by $2$ but not by $3$ , it is not divisible by $6$ .

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