Count of natural numbers in range [L, R] which are relatively prime with N
Given three integers N, L, and R. The task is to calculate the number of natural numbers in the range [L, R] (both inclusive) which are relatively prime with N.
Input: N = 10, L = 1, R = 25
10 natural numbers (in the range 1 to 25) are relatively prime to 10.
They are 1, 3, 7, 9, 11, 13, 17, 19, 21, 23.
Input: N = 12, L = 7, R = 38
11 natural numbers (in the range 1 to 38) are relatively prime to 12.
They are 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37.
- At first, factorize the number N. Thus, find out all the prime factors of N.
- Store prime factors of the number N in an array.
- We can determine the total number of natural numbers which are not greater than R and are divisible by prime factors of N.
- Suppose that the value is y. So, exactly y natural numbers not greater than R have at least a single common divisor with N.
- So, these y numbers can not be relatively prime to N.
- Thus, the number of natural number not greater than R which are relatively prime to N will be R – y .
- Now, similarly we need to find out the number of relatively prime numbers of N which are not greater than L-1.
- Then, subtract the result for L-1 from the answer for R.
Below is the implementation of the above approach: