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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 $99,101,999,1001,999\text{ and }1001$

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

(a) Enter dividend: $29918$

(b) Select divisor: $7$

(c) Click on “Check”

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

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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