Question

Find the sum of all the no which are co prime to 60 and less then 60

Answer 1

For every such coprime number A, there is another coprime number (60 - A). So we will count all the numbers coprime to 30, and multiply by 60.

For every number B coprime to 30, there is another coprime number (30 - B). So we will count all the ODD numbers coprime to 15, and double it.

1 + 7 + 11 + 13 = 4 numbers, double it gives 8 numbers less than 30, and for every such number there is a pair of numbers which add to 60, therefore the answer is 8 * 60 = 480.

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