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------------------------------------------------ How many positive integers from 1 to 143 are relatively prime to 143? In other words, compute \(\varphi(143)\).

Note: \(11 \times 13 = 143\).

Answer :

Final answer:

There are 120 positive integers from 1 to 143 that are relatively prime to 143.

Explanation:

In order to find the number of positive integers that are relatively prime to 143, we need to find the number of integers that do not share any common factors with 143 other than 1. Since 143 can be expressed as the product of its prime factors, 11 and 13, we can use the formula (p-1) * (q-1) to calculate the number of relatively prime integers.

In this case, p = 11 and q = 13, so (p-1)(q-1) = (11-1)(13-1) = 10 * 12 = 120.

Therefore, there are 120 positive integers from 1 to 143 that are relatively prime to 143.

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