Multiples and Relatively Prime Numbers.
Number Theory
Level
pending
How many numbers between 1 and 10000 are a multiple of 18 and relatively prime to 306?
The answer is 0.
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1 solution
It is zero because 3 0 6 = 1 8 ⋅ 1 7 . Therefore all natural numbers between 1 and 1 0 0 0 0 that are a multiple of 1 8 can never be relatively prime to 3 0 6 since g cd ( 1 8 x , 3 0 6 ) = 1 8 .