2021 AMC 12B Problems/Problem 7
Contents
Problem
Let . What is the ratio of the sum of the odd divisors of
to the sum of the even divisors of
?
Solution
Prime factorize to get
. For each odd divisor
of
, there exist even divisors
of
, therefore the ratio is
Solution
Prime factorizing , we see
. The sum of
's odd divisors are the sum of the factors of
without
, and the sum of the even divisors is the sum of the odds subtracted by the total sum of divisors. The sum of odd divisors is given by
and the total sum of divisors is
. Thus, our ratio is
~JustinLee2017
Video Solution by OmegaLearn (Prime Factorization)
~ pi_is_3.14
See Also
2021 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 6 |
Followed by Problem 8 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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