Definition
Divisibility
Divisibility tells whether one whole number can be divided by another with no remainder.
Continue from this idea into connected AXIO math.
Boundary check: Zero remainder is essential; division by zero is never allowed.
What it means
Divisibility is an exact-sharing test. If a number can be split into equal groups of the chosen size with nothing left over, it is divisible by that size. A remainder means it is not divisible.
Remember it
Divisible means equal groups with zero left over.
Example
Eighty-four is divisible by 7 because 84 ÷ 7 = 12 with remainder 0. The multiplication check is 7 × 12 = 84.
Watch for
The divisor cannot be 0 because division by zero is undefined. Zero is divisible by every nonzero whole number because 0 = b × 0.
Common mix-up
If 84 is divisible by 7, then 7 is a factor of 84 and 84 is a multiple of 7. These statements describe the same exact relationship from different directions.
Exact meaning
For whole numbers a and b with b not equal to 0, a is divisible by b when a = b × k for some whole number k. Equivalently, a ÷ b has a whole-number quotient and remainder 0.