Discrete Maths:- Test series

Question

Number of positive integer less than equal to 1000 that are relatively prime to 15?

Answer 1

Relatively prime means not divisible by 3 or 5

First we will find non relative primes that means

Numbers divisible by 3 or 5 between 1 - 1000  N(X) = Ceil(1000/3) + Ceil(1000/5) - Ceil(1000/3 *5)

                                                                        = 333 + 200 -66 = 467

Now relatively prime means N(x)' = 1000 - 467 = 533

Comments

Can you explain why not divisible by 3 or 5?

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Two integers are relatively prime if they share no common positive factors (divisors) except 1. Here we want relative prime of 15 so we did factorization of 15. 15 = 5x 3 .If the numbers are not divisible by both 3 and 5 then they will not be divisible by 15.