Answer :
The number of positive integers from 1 to 143 that are relatively prime to 143, we need to compute the Euler's totient function of 143, denoted as φ(143). The Euler's totient function calculates the count of positive integers less than or equal to a given number that are coprime to it.
1. Decompose 143 into its prime factors: 143 = 11 × 13.
2. Apply Euler's totient function formula: φ(n) = n × (1 - 1/p₁) × (1 - 1/p₂) × ... × (1 - 1/pₙ), where p₁, p₂, ..., pₙ are the distinct prime factors of n.
3. Substitute the prime factors of 143 into the formula: φ(143) = 143 × (1 - 1/11) × (1 - 1/13) = 143 × (10/11) × (12/13) = 120.
4. Therefore, there are 120 positive integers from 1 to 143 that are relatively prime to 143.
By applying Euler's totient function and calculating φ(143), we find that there are 120 positive integers from 1 to 143 that are relatively prime to 143.
Learn more about prime factors: brainly.com/question/29775157
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