2021 JMPSC Accuracy Problems/Problem 1: Difference between revisions
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== Solution == | == Solution == | ||
We use the fact that <math>27 = | We use the fact that <math>3 = 3^1</math> and <math>27 = 3^3</math> to conclude that the only multiples of <math>3</math> that are factors of <math>27</math> are <math>3</math>, <math>9</math>, and <math>27</math>. Thus, our answer is <math>3 + 9 + 27 = \boxed{39}</math>. | ||
~Bradygho | ~Bradygho | ||
== Solution 2 == | |||
The factors of <math>27</math> are <math>1</math>, <math>3</math>, <math>9</math> and <math>27</math>. Out of these, only <math>3</math>, <math>9</math> and <math>27</math> are multiples of <math>3</math>, so the answer is <math>3 + 9 + 27 = \boxed{39}</math>. | |||
Revision as of 10:22, 11 July 2021
Problem
Find the sum of all positive multiples of 
that are factors of 
Solution
We use the fact that 
and 
to conclude that the only multiples of that are factors of 
are , 
, and . Thus, our answer is 
.
~Bradygho
Solution 2
The factors of are 
, , and . Out of these, only , and are multiples of , so the answer is .
