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## Test for Divisibility

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**It’s often useful to know whether one number
is evenly divisible by another number. Here are some tricks that go
beyond knowing whether a number is odd or even, or divisible by
10.**

Before decimals such as 3.5 were invented, people had to
use numbers with fractional parts instead, such as
3^{1}/^{2}. In many
division problems, they had to reduce fractions with large numbers—for
example, 243 / 405—to their lowest terms—in this case,
^{3}/^{5}. Knowing rules
to determine divisibility by the integers from 1 through 12, or from 1
through 15, was very useful in that precalculator
time.^{1}

If you want to strengthen your mental math powers, knowing the
same rules can be useful to you today. In particular, these rules are
helpful with math tricks that involve factoring numbers, such as simplified mental
multiplication. Sometimes, knowing *that* a number is
evenly divisible by another number goes at least halfway toward knowing
*what* the answer is.