2021 JMPSC Accuracy Problems/Problem 1

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Problem

Find the sum of all positive multiples of $3$ that are factors of $27.$

Solution

We use the fact that $3 = 3^1$ and $27 = 3^3$ to conclude that the only multiples of $3$ that are factors of $27$ are $3$, $9$, and $27$. Thus, our answer is $3 + 9 + 27 = \boxed{39}$.

~Bradygho

Solution 2

The factors of $27$ are $1$, $3$, $9$ and $27$. Out of these, only $3$, $9$ and $27$ are multiples of $3$, so the answer is $3 + 9 + 27 = \boxed{39}$.

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