Answer :
Final answer:
The number of integers between 1 and 143 that are relatively prime to 143 is 120, as calculated by Euler's totient function, applying the formula (p-1)(q-1) for a product of two distinct prime numbers p and q. The given options do not match the correct answer, indicating a potential error in the question or options provided.
Explanation:
The question is asking for the number of integers between 1 and 143 that are relatively prime to 143. Two numbers are relatively prime if they share no common divisors other than 1. The number 143 can be factored into its prime factors, which are 11 and 13. The count of numbers relatively prime to 143 is given by Euler's totient function, which for a number that is the product of two distinct primes p and q, is calculated as [tex]\(\phi(n)=(p-1)(q-1)\).[/tex]
Applying this to 143, we have [tex]\(\phi(143)=(11-1)(13-1)=10\times12=120\).[/tex]
Therefore, there are 120 numbers between 1 and 143 that are relatively prime to 143, which is not one of the provided options.
