How this calculator works
An integer is divisible by d if division leaves remainder zero. The detailed view writes an exact quotient-remainder identity; the summary checks twelve small divisors. Negative inputs use non-negative remainders with a positive divisor. The summary is shown as readable text rather than an interactive table.
Formula
n = dq + r, with 0 <= r < d. The condition d | n is equivalent to r = 0.
Worked example
156 is divisible by 3 because 156 = 3 × 52. It is not divisible by 5 because 156 = 5 × 31 + 1.
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Frequently asked questions
Is zero divisible by these divisors?
Yes. Zero equals each non-zero divisor multiplied by zero.
Does a negative sign change divisibility?
No. If d divides n, it also divides -n.
Can digit rules replace division?
Often. Divisibility by 3 or 9 can be checked with a digit sum, and by 2 with the final digit. Exact remainders provide a common check for every listed divisor.