2021 JMPSC Accuracy Problems/Problem 1

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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2021 JMPSC Accuracy Problems/Problem 1

Problem

Solution

Solution 2