Answer :
Final answer:
The number of integers that are relatively prime to 143 within the range of 1 to 143 is 120, determined by Euler's totient function and the prime factorization of 143.
Explanation:
The question asks for the number of integers in the range 1 to 143 that are relatively prime with 143. To determine this, we must first factor 143 to find its prime factors. The number 143 can be factored into 11 and 13. Thus, any number that is not a multiple of 11 or 13 will be relatively prime with 143. Using the concept of the Euler's totient function, we know that the count of numbers relatively prime to 143 will be ϕ(143), which is (11-1)×(13-1) since 11 and 13 are prime numbers. This yields 10× 12 = 120. Therefore, there are 120 numbers from 1 to 143 that are relatively prime with 143, which is not one of the provided options. It seems there might be a misunderstanding either in the question or the answer choices provided.
