Numbers by Prabhav (Part:3)

Number Theory Level pending

Find the number of positive integers less than equal to 3600 that are co prime to 3600.


The answer is 960.

Prabhav Bansal by Prabhav Bansal , 28, India

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1 solution

Otto Bretscher
Sep 4, 2015

It's ϕ ( 3600 ) = ϕ ( 2 4 × 3 2 × 5 2 ) = ( 2 4 − 2 3 ) ( 3 2 − 3 1 ) ( 5 2 − 5 1 ) = 960. \phi(3600)=\phi(2^4\times{3^2}\times{5^2})=(2^4-2^3)(3^2-3^1)(5^2-5^1)=960.

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