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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 \(3\)?
Your answer
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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

Use the divisibility rule

\[342~\text{is}~\text{divisible}~by~3~\text{if}~3~+~4~+~2~\text{is}~\text{divisible}~by~3\]

The divisibility rule for 3 says a whole number is divisible by 3 exactly when its digit sum is divisible by 3.

02

Add the digits

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

The digits of the prompt number 342 are 3, 4, and 2. Their sum is 9.

03

Test the digit sum

\[9~/~3~=~3\]

Nine is divisible by 3 because its quotient is the whole number 3. Therefore 342 passes the divisibility rule.

04

Check with direct division

\[342~/~3~=~114\]

Direct division gives the whole-number quotient 114 with no remainder, confirming the digit-sum conclusion.

05

Classify the number

\[\text{divisible}\]

Since 342 divides evenly by 3, the required classification is divisible. This matches the correct choice.

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Another way

  1. Split 342 as 300 + 42; both terms are divisible by 3, so their sum is divisible by 3.

!

Common mistake

Do not require the digit sum to equal 3. It only needs to be divisible by 3; here the sum 9 qualifies.

Solution walkthrough video