Answer :

Final answer:

There are 120 numbers between 1 and 143 that are relatively prime to 143. This is calculated using Euler's totient function since 143 is the product of two prime numbers, 11 and 13.

Explanation:

The question asks how many numbers between 1 and 143 are relatively prime with 143. Two numbers are relatively prime if their greatest common divisor (GCD) is 1. The number 143 can be factored into the prime numbers 11 and 13 (143 = 11 * 13), so any number that is not a multiple of either 11 or 13 will be relatively prime to 143.

To find the count of numbers that are relatively prime to 143, we can use Euler's totient function, φ(n), which gives the count of numbers less than n that are relatively prime to n. When n is a product of two distinct prime numbers p and q, the totient function is calculated as φ(n) = (p - 1) * (q - 1). In this case:

φ(143) = (11 - 1) * (13 - 1) = 10 * 12 = 120

Therefore, there are 120 numbers between 1 and 143 that are relatively prime to 143, so the correct answer is C. 120.

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