2016 AMC 8 Problems/Problem 9
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Problem
What is the sum of the distinct prime integer divisors of ?
Solution 1
The prime factorization is . Since the problem is only asking us for the distinct prime factors, we have
. Their desired sum is then
.
Solution 2
We notice that , since
, and
. We can divide
by
to get
. This is divisible by
, as
. Dividing
by
, we have
. This is clearly divisible by
, leaving
. We have
. We know that
and
are both multiples of
,
is
, and
is prime. This means that the distinct prime factors are
and
. Their sum is
.
2016 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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