Divisibility Calculator (step-by-step solution)

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select divisor
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Quick Start Guide

Overview

Divisibility calculator determines if a number is divisible by another number without actually performing the division. For this, it uses the defined divisibility rules.

It displays all the steps used for the calculation.

This calculator supports
(a) divisibility rules of $2,3,\cdots 47$
(b) divisibility rules of $99,101,999,1001,999\text{ and }1001$

Usage

Input the dividend, select the divisor and click on “Check”. The results will be displayed at the bottom. A random example can be generated using the "e.g." link at the top

Example: Check if 29918 is divisible by 7

(a) Enter dividend: $29918$
(b) Select divisor: $7$
(c) Click on “Check”

Divisible By

A number $x$ is divisible by another number $y$ if $x$ ÷ $y$ gives remainder $0$
Examples
(a) $8$ is divisible by $2$
(b) $9$ is not divisible by $2$

Divisibility Rules

Divisibility rules helps to find out whether a number is divisible by another number without performing the division. (more details)

Divisibility Rules in Short

 Number Divisible by Rule abcdef $2$ If 'f' is even abcdef $3$ If '(a+b+c+d+e+f)' is divisible by $3$(apply this rule again and again if necessary) abcdef $4$ If 'ef' is divisible by $4$ abcdef $5$ If 'f' is $0$ or $5$ abcdef $6$ If 'abcdef' is divisible by $2$ and $3$ abcdef $7$ If 'abcde-$2$×f' is divisible by $7$(apply this rule again and again if necessary) abcdef $8$ If 'def' is divisible by $8$ abcdef $9$ If 'a+b+c+d+e+f' is divisible by $9$(apply this rule again and again if necessary) abcdef $10$ If 'f' is $0$ abcdef $11$ If 'f-e+d-c+b-a' is divisible by $11$ abcde $11$ If 'e-d+c-b+a' is divisible by $11$ abcdef $12$ if 'abcdef' is divisible by $3$ and $4$ abcdef $13$ If 'abcde+$4$×f' is divisible by $13$(apply this rule again and again if necessary) abcdef $14$ if 'abcdef' is divisible by $2$ and $7$ abcdef $15$ if 'abcdef' is divisible by $3$ and $5$ abcdef $16$ If 'cdef' is divisible by $16$ abcdef $17$ If 'abcde-$5$×f' is divisible by $17$(apply this rule again and again if necessary) abcdef $18$ if 'abcdef' is divisible by $2$ and $9$ abcdef $19$ If 'abcde+$2$×f' is divisible by $19$(apply this rule again and again if necessary) abcdef $20$ If 'f' is $0$ and 'e' is even abcdef $21$ if 'abcdef' is divisible by $3$ and $7$ abcdef $22$ if 'abcdef' is divisible by $2$ and $11$ abcdef $23$ If 'abcde+$7$×f' is divisible by $23$(apply this rule again and again if necessary) abcdef $24$ if 'abcdef' is divisible by $3$ and $8$ abcdef $25$ If 'ef' is divisible by $25$ abcdef $26$ if 'abcdef' is divisible by $2$ and $13$ abcdef $27$ If '(abcde)-$8$×f is divisible by $27$(apply this rule again and again if necessary) abcdef $28$ If 'abcdef is divisible by $4$ and $7$ abcdef $29$ If 'abcde+$3$×f is divisible by $29$ abcdef $30$ If 'abcdef is divisible by $3$ and $10$ abcdef $31$ If 'abcde-$3$×f is divisible by $31$(apply this rule again and again if necessary) abcdef $32$ If 'bcdef' is divisible by $32$ abcdef $33$ if 'abcdef' is divisible by $3$ and $11$ abcdef $34$ if 'abcdef' is divisible by $2$ and $17$ abcdef $35$ if 'abcdef' is divisible by $5$ and $7$ abcdef $36$ if 'abcdef' is divisible by $4$ and $9$ abcdef $37$ If 'abcde-$11$×f' is divisible by $37$(apply this rule again and again if necessary) abcdef $38$ if 'abcdef' is divisible by $2$ and $19$ abcdef $39$ if 'abcdef' is divisible by $3$ and $13$ abcdef $40$ if 'abcdef' is divisible by $5$ and $8$ abcdef $41$ If 'abcde-$4$×f' is divisible by $41$ abcdef $42$ if 'abcdef' is divisible by $2,3$ and $7$ abcdef $43$ If 'abcde+$13$×f' is divisible by $43$(apply this rule again and again if necessary) abcdef $44$ if 'abcdef' is divisible by $4$ and $11$ abcdef $45$ if 'abcdef' is divisible by $5$ and $9$ abcdef $46$ if 'abcdef' is divisible by $2$ and $23$ abcdef $47$ If 'abcde-$14$×f' is divisible by $47$(apply this rule again and again if necessary) abcdef $99$ If 'ef+cd+ab' is divisible by $99$(of the form $10^2-1.$ groups of $2$ digits from right, $++++\cdots$) abcde $99$ If 'de+bc+a' is divisible by $99$(of the form $10^2-1.$ groups of $2$ digits from right, $++++\cdots$) abcdef $101$ if 'ef-cd+ab' is divisible by $101$(of the form $10^2+1.$ groups of $2$ digits from right, $-+-+\cdots$) abcde $101$ if 'de-bc+a' is divisible by $101$(of the form $10^2+1.$ groups of $2$ digits from right, $-+-+\cdots$) abcdef $999$ if def+abc' is divisible by $101$(of the form $10^3-1.$ groups of $3$ digits from right, $++++\cdots$) abcde $999$ if cde+ab' is divisible by $999$(of the form $10^3-1.$ groups of $3$ digits from right, $++++\cdots$) abcdef $1001$ if 'def-abc' is divisible by $1001$(of the form $10^3+1.$ groups of $3$ digits from right, $-+-+\cdots$) abcde $1001$ if 'cde-ab' is divisible by $1001$(of the form $10^3+1.$ groups of $3$ digits from right, $-+-+\cdots$) abcdef $9999$ if 'cdef+ab' is divisible by $9999$(of the form $10^4-1.$ groups of $4$ digits from right, $++++\cdots$) abcde $9999$ if 'bcde+a' is divisible by $9999$(of the form $10^4-1.$ groups of $4$ digits from right, $++++\cdots$) abcdef $10001$ if 'cdef-ab' is divisible by $10001$(of the form $10^4+1.$ groups of $4$ digits from right, $-+-+\cdots$) abcde $10001$ if 'bcde-a' is divisible by $10001$(of the form $10^4+1.$ groups of $4$ digits from right, $-+-+\cdots$)

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