A $\mathbf{divisibility\ test}$ is a quick way to tell whether one number is divisible by another,

Question

A $\mathbf{divisibility\ test}$ is a quick way to tell whether one number is divisible by another, without actually performing the division. Divisible by Rule / How to Test Example $2$Last digit is even ($0$, $2$, $4$, $6$, $8$).$246 \rightarrow 6$ is even $\rightarrow$ divisible by $2$ $3$Sum of digits is divisible by $3$.$342 \rightarrow 3+4+2=9 \rightarrow$ divisible by $3$ $4$Last two digits form a number divisible by $4$.$312 \rightarrow 12 \div 4 = 3 \rightarrow$ divisible by $4$ $5$Last digit is $0$ or $5$.$135 \rightarrow$ ends with $5 \rightarrow$ divisible by $5$ $6$Number is divisible by both $2$ and $3$.$54 \rightarrow$ even, and $5+4=9 \rightarrow$ divisible by $6$ $7$Double the last digit and subtract it from the rest of the number. If the result is divisible by $7$, so is the original number.$203 \rightarrow 20 - (2 \times 3) = 14 \rightarrow 14 \div 7 = 2 \rightarrow$ divisible by $7$ $8$Last three digits form a number divisible by $8$.$1416 \rightarrow 416 \div 8 = 52 \rightarrow$ divisible by $8$ $9$Sum of digits is divisible by $9$.$4,185 \rightarrow 4+1+8+5=18 \rightarrow 18 \div 9 = 2 \rightarrow$ divisible by $9$ $10$Last digit is $0$.$670 \rightarrow$ ends with $0 \rightarrow$ divisible by $10$

Accepted Answer

The divisibility tests for $2$ to $10$ are given in the typed solution.

Divisible by	Rule / How to Test	Example
\(2\)	Last digit is even (\(0\), \(2\), \(4\), \(6\), \(8\)).	\(246 \rightarrow 6\) is even \(\rightarrow\) divisible by \(2\)
\(3\)	Sum of digits is divisible by \(3\).	\(342 \rightarrow 3+4+2=9 \rightarrow\) divisible by \(3\)
\(4\)	Last two digits form a number divisible by \(4\).	\(312 \rightarrow 12 \div 4 = 3 \rightarrow\) divisible by \(4\)
\(5\)	Last digit is \(0\) or \(5\).	\(135 \rightarrow\) ends with \(5 \rightarrow\) divisible by \(5\)
\(6\)	Number is divisible by both \(2\) and \(3\).	\(54 \rightarrow\) even, and \(5+4=9 \rightarrow\) divisible by \(6\)
\(7\)	Double the last digit and subtract it from the rest of the number. If the result is divisible by \(7\), so is the original number.	\(203 \rightarrow 20 - (2 \times 3) = 14 \rightarrow 14 \div 7 = 2 \rightarrow\) divisible by \(7\)
\(8\)	Last three digits form a number divisible by \(8\).	\(1416 \rightarrow 416 \div 8 = 52 \rightarrow\) divisible by \(8\)
\(9\)	Sum of digits is divisible by \(9\).	\(4,185 \rightarrow 4+1+8+5=18 \rightarrow 18 \div 9 = 2 \rightarrow\) divisible by \(9\)
\(10\)	Last digit is \(0\).	\(670 \rightarrow\) ends with \(0 \rightarrow\) divisible by \(10\)

Divisibility Test

Divisibility Test

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