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All courses Math Foundations · MF.NS.6 6 of 60
Use divisibility rules, prime factorization, and factor structure to analyze and solve whole-number problems.

Check divisibility with one rule

Problem
Is 342 divisible by 3? Answer divisible or not divisible.
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Hint

Use the divisibility rule for 3: add the digits in 342.

A whole number is divisible by 3 if the sum of its digits is divisible by 3.

Solution walkthrough

01

Identify the rule for 3

\[\text{Divisor}:~3\]

To test divisibility by 3, add the digits of the number. If that sum is divisible by 3, then the whole number is divisible by 3.

02

Add the digits of 342

\[3~+~4~+~2~=~9\]

The divisibility rule for 3 uses the digit sum, so we add the digits in 342.

03

Check the digit sum

\[9~÷~3~=~3\]

Since 9 is divisible by 3, the original number passes the divisibility test.

04

State the result

\[342~\text{is}~\text{divisible}~\text{by}~3\]

Yes. The digit sum is 9, and 9 is divisible by 3, so 342 is divisible by 3.

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Another way

  1. You can also notice that 342 = 300 + 42, and both 300 and 42 are divisible by 3, so 342 is divisible by 3.

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Common mistake

A common mistake is checking only the last digit and saying 342 is not divisible by 3 because it ends in 2. The last-digit test is for 2, not for 3.