Unlucky 13

Number Theory Level 1

What is the smallest integer that is greater than 100 and is a multiple of 13?


The answer is 104.

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Arron Kau by Arron Kau

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2 solutions

Arron Kau Staff
May 13, 2014

Solution : We can check that 100 = 7 × 13 + 9 100 = 7 \times 13 + 9 , hence the smallest multiple of 13 will be 8 × 13 = 104 8 \times 13 = 104 .

Solution 2: We can list the multiples of 13 out as 13 , 26 , 39 , 52 , 65 13, 26, 39, 52, 65 , 78 , 91 , 104 , … 78, 91, 104, \ldots , hence the smallest multiple of 13 will be 104 104 .

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Matthew Hayes
Sep 5, 2015

13*100=130

130-13-13=104

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