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Without dividing, determine if 96,090 is divisible by 6 and explain how you know.

96,090◻" divisible by "6

Without dividing, determine if $96$ , $090$ is divisible by $6$ and explain how you know. $\newline$ $96,090 \square \text { divisible by } 6$

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Solve complex trigonomentric equations

Full solution

Q. Without dividing, determine if

96

,

090

is divisible by

6

and explain how you know.

\newline

96,090 \square \text { divisible by } 6

Check Divisibility by $2$ : To determine if a number is divisible by $6$ , it must be divisible by both $2$ and $3$ . For a number to be divisible by $2$ , it must be even, which means its last digit must be $0$ , $2$ , $4$ , $6$ , or $8$ . For a number to be divisible by $3$ , the sum of its digits must be divisible by $3$ . $\newline$ Let's first check if $96,090$ is divisible by $2$ .
Check Divisibility by $3$ : The last digit of $96,090$ is $0$ , which is an even number. Therefore, $96,090$ is divisible by $2$ .
Check Sum of Digits: Now let's check if $96,090$ is divisible by $3$ by adding its digits: $9 + 6 + 0 + 9 + 0 = 24$ .
Verify Divisibility by $6$ : The sum of the digits, $24$ , is divisible by $3$ because $24 \div 3 = 8$ , which is a whole number.
Verify Divisibility by $6$ : The sum of the digits, $24$ , is divisible by $3$ because $24 \div 3 = 8$ , which is a whole number.Since $96,090$ is divisible by both $2$ and $3$ , we can conclude that $96,090$ is divisible by $6$ .

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