2021 JMPSC Accuracy Problems/Problem 11
Problem
If and
,
,
, and
are divisors of
, what is the maximum value of
?
Solution 1
must be a number such that
,
,
. Thus, we must have
. This implies the maximum value of
is
, which works.
~Bradygho
Solution 2
Notice that . Because
and
it is invalid for
to be a multiple of
. With similar reasoning,
must have at most one factor of
. Thus,
.
(With , we have
which is valid)
~Apple321
Solution 3 (A Little Bashy)
Note , so the divisors are
. We see the set
is the largest 4-digit set we can form, so the answer is
~Geometry285