Members of the Family

Number Theory Level 2

How many members of the set 1 7 , 2 7 , 3 7 . . . , 99 7 \frac{1}{7},\frac{2}{7},\frac{3}{7}...,\frac{99}{7} are integer multiples of 2 5 \large\frac{2}{5} ?

10 7 1 8 0

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Hana Wehbi
Mar 7, 2017

If a 7 = k 2 5 \frac{a}{7}=k\frac{2}{5} , then 14 k = 5 a 14k=5a , so a a must be a multiple of 14 14 . There are 7 7 such numbers less than 100 100

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