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Find the number of distinct fractions a/b, where both a & b are integers with 0<=a<=b<=50 and gcd(a,b) = 1?

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Find the number of distinct fractions a/b, where both a & b are integers with 0<=a<=b<=50 and gcd(a,b) = 1?
posted Jun 9, 2017 by anonymous

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1 Answer

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gcd of (a,b)=1 implies one of a or b is 1. Thus these fractions are 1/2, 1/3................ 1/50 49 of these
Also the prime numbers are 1,2,3,5,7,11,13,17,19,23,29,31,37,41,43,47
when 2 is divided by 3,5 .......47 we get 14 fractions with numerator 2 and gcd of fraction integers as 1.
Similarly with 3 as numerator we get 13 fractions
Similarly with 5 as numerator we get 12 fractions
Similarly with 7 as numerator we get 11 fractions
Similarly with11 as numerator we get 10 fractions
Similarly with 13 as numerator we get 9 fractions
Similarly with 17 as numerator we get 8 fractions
Similarly with 19 as numerator we get 7 fractions
Similarly with 23 as numerator we get 6 fractions
Similarly with 29 as numerator we get 5 fractions
Similarly with31 as numerator we get 4 fractions
Similarly with 37 as numerator we get 3 fractions
Similarly with 41as numerator we get 2 fractions
Similarly with 43as numerator we get 1 fractions
With prime numbers we get 105 fractions
Tptal=199 if fraction means less than one

answer Jun 17, 2017 by Kewal Singh Paneser
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