A divisibility check is a remainder check. If nothing is left over, the division is exact.
⚠Note: The divisor cannot be zero. A number is divisible by a divisor only when the remainder is exactly zero.
How Divisibility Works
Divisibility means one integer can be divided by another without a remainder. It is one of the basic tests used in factoring, fractions, and number theory.
Exact Division
If a / b is an integer, then a is divisible by b.
Remainder Test
The fastest general test is checking whether a mod b equals 0.
Factor Meaning
If b divides a, then b is a factor of a.
Quotient Check
When divisible, the quotient gives the matching factor pair.
Example: 84 is divisible by 7 because 84 mod 7 = 0 and 84 = 7 x 12.
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