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Without dividing, determine if 69,284 is divisible by 3 and explain how you know.

69,284◻ divisible by 3

Without dividing, determine if $69$ , $284$ is divisible by $3$ and explain how you know. $\newline$ $69,284 \square$ divisible by $3$

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Evaluate two-variable equations: word problems

Full solution

Q. Without dividing, determine if

69

,

284

is divisible by

3

and explain how you know.

\newline

69,284 \square

divisible by

3

Use Divisibility Rule: To determine if a number is divisible by $3$ , we can use the divisibility rule for $3$ , which states that a number is divisible by $3$ if the sum of its digits is divisible by $3$ .
Add Digits Together: First, we add the digits of $69,284$ together: $6 + 9 + 2 + 8 + 4$ .
Calculate Sum: Calculating the sum of the digits: $6 + 9 = 15$ , $15 + 2 = 17$ , $17 + 8 = 25$ , $25 + 4 = 29$ .
Check Divisibility: Now we need to determine if the sum of the digits, which is $29$ , is divisible by $3$ .
Final Conclusion: Since $29$ is not divisible by $3$ (because $3 \times 9$ is $27$ , and $29$ is not a multiple of $3$ ), we can conclude that $69,284$ is not divisible by $3$ .

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