Divisibility Test Calculator

Enter whole numbers and review common divisibility rules. See remainders, charts, exports, and quick checks. Learn patterns clearly through examples and stepwise explanations today.

Calculator form

Whole number

Custom divisor

Sort results by

Graph metric

Include standard tests 2 through 12

Show working values and rule notes

Display only passed tests

Formula used

General divisibility formula

n is divisible by d when n mod d = 0

Reliable long-division remainder update

r(next) = (10 × r(current) + next digit) mod d

2: last digit is even.
3: digit sum is divisible by 3.
4: last two digits form a multiple of 4.
5: last digit is 0 or 5.
6: the number is divisible by both 2 and 3.
7: the calculator confirms the exact remainder directly.
8: last three digits form a multiple of 8.
9: digit sum is divisible by 9.
10: last digit is 0.
11: alternating digit sum is a multiple of 11.
12: the number is divisible by both 3 and 4.

How to use this calculator

Enter any whole number, including very large values.
Optionally add a custom divisor larger than 1.
Keep the standard suite enabled to test 2 through 12.
Choose whether to sort by divisor or by pass status.
Select the graph metric to plot remainders or pass flags.
Press Check divisibility to show the result block above the form.
Review the summary, table, working values, and graph.
Download the report as CSV or PDF if needed.

Example data table

Number	Passed tests	Why it passes
128	2, 4, 8	It ends in 8, the last two digits are 28, and the last three digits are 128.
135	3, 5, 9	The digit sum is 9 and the last digit is 5.
462	2, 3, 6, 7, 11	It is even, its digit sum is 12, and direct remainder checks confirm 7 and 11.
660	2, 3, 4, 5, 6, 10, 11, 12	It is even, ends in 0, digit sum is 12, and the last two digits are 60.
121	11	The alternating sum rule confirms a multiple of 11.

FAQs

1) What does divisibility mean?

A number is divisible by another number when the remainder is zero after division. For example, 24 is divisible by 6 because 24 ÷ 6 leaves no remainder.

2) Can I test negative numbers?

Yes. Divisibility rules depend on the absolute value. A negative whole number has the same divisibility results as its positive counterpart for the same divisor.

3) Is zero divisible by every divisor shown?

Yes. Zero divided by any nonzero positive divisor gives remainder zero. This calculator therefore marks zero as divisible by every selected divisor greater than zero.

4) Why are digit sums useful?

Digit sums simplify checks for 3 and 9. If the digit sum is divisible by 3 or 9, the whole number is also divisible by 3 or 9.

5) Why does the calculator use exact remainders for 7?

The divisibility rule for 7 is less convenient mentally. Exact remainder calculation is dependable, fast, and avoids confusion from shortcut methods when numbers become large.

6) What is the alternating sum rule for 11?

Starting from the right, alternate plus and minus signs across the digits. If that total is a multiple of 11, the number is divisible by 11.

7) Can I test very large numbers?

Yes. The calculator processes digits directly instead of relying on normal integer limits. That approach supports much larger whole numbers safely and accurately.

8) What do the CSV and PDF exports contain?

They capture the checked number, summary values, and the result table. CSV is useful for spreadsheets, while PDF is better for printing or sharing a report.