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Without dividing, determine if 47,734 is divisible by 6 and explain how you know.

47,734◻ divisible by 6

Without dividing, determine if $47$ , $734$ is divisible by $6$ and explain how you know. $\newline$ $47,734 \square$ divisible by $6$

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Evaluate two-variable equations: word problems

Full solution

Q. Without dividing, determine if

47

,

734

is divisible by

6

and explain how you know.

\newline

47,734 \square

divisible by

6

Check for Even Last Digit: To determine if a number is divisible by $6$ , it must be divisible by both $2$ and $3$ . 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 $8$ .
Divisibility by $2$ : Looking at the last digit of $47,734$ , which is $4$ , we can see that it is even. Therefore, $47,734$ is divisible by $2$ .
Sum of Digits for Divisibility: 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 $3$ . We will add the digits of $47,734$ and check if the sum is divisible by $3$ .
Check Divisibility by $3$ : Adding the digits of $47,734$ : $4 + 7 + 7 + 3 + 4 = 25$ . Now we need to determine if $25$ is divisible by $3$ .
Final Divisibility Conclusion: Since $25$ is not divisible by $3$ (because $3 \times 8$ is $24$ and $3 \times 9$ is $27$ , and $25$ does not fall in the $3$ 's multiplication table), $47,734$ is not divisible by $3$ .
Final Divisibility Conclusion: Since $25$ is not divisible by $3$ (because $3 \times 8$ is $24$ and $3 \times 9$ is $27$ , and $25$ does not fall in the $3$ 's multiplication table), $47,734$ is not divisible by $3$ .Because $47,734$ is not divisible by $3$ , it cannot be divisible by $3$ $2$ , as a number must be divisible by both $3$ $3$ and $3$ to be divisible by $3$ $2$ . Therefore, $47,734$ is not divisible by $3$ $2$ .

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