Legendre’s formula:
The exponent of in the prime factorization of
is
This is equivalent to:
Explanation: Between and
there are
numbers that are multiples of
:
. (e.g. if
and
, these are
.) These each contribute a factor of
. Of those, there are
multiples of
that each contribute one more factor of
. (e.g. one more:
. 4 factors in total.) The multiples of
contribute one more factor, etc until
.
Example: Find the exponent of in the prime factorization of
.