We say that divides , or that is a multiple of , if there is an integer such that . In this case, we write and say that is a divisor of . If does not divide , we write .
e.g. , so and .
Knuth et al in Concrete Mathematics use and say “The notation `m|n’ is actually much more common than `m\n’ in current mathematics literature. But vertical lines are overused – for absolute values, set delimiters, conditional probabilities, etc. – and backward slashes are underused. Moreover, `m\n’ gives an impression that m is the denominator of an implied ratio. So we shall boldly let our divisibility symbol lean leftward.”
greatest common divisor
The greatest common divisor of two positive integers and , written , is the largest number that divides evenly (no remainder) into both. If and have no common factor, .
is defined as
means rounded up to the next-highest integer.
means rounded down. e.g. and