What is value of Euler's Phi function in RSA if the primes are 7 and 11 ?

Euler's totient function φ(n) counts the positive integers from 1 to n that are coprime to n. When the modulus is built as n = p × q from two distinct primes p and q, φ is multiplicative over the coprime factors p and q, and φ(prime) = prime − 1 for any prime. Combining these two facts gives the closed-form identity φ(n) = (p − 1)(q − 1), which is exactly the totient RSA key generation needs.

1. Identify the two given primes: p = 7 and q = 11.

2. Apply the identity for the totient of an RSA modulus: φ(n) = (p − 1)(q − 1).

3. Substitute the prime values: φ(n) = (7 − 1)(11 − 1) = 6 × 10.

4. Evaluate the product: φ(n) = 60.

As an independent check, compute n = p × q = 7 × 11 = 77 and count directly how many integers from 1 to 77 share a factor with 77. Multiples of 7 up to 77 number 11, multiples of 11 number 7, and the single multiple of 77 itself is counted in both groups, so by inclusion–exclusion 11 + 7 − 1 = 17 integers are NOT coprime to 77. Subtracting from the total gives 77 − 17 = 60 integers that ARE coprime to 77, matching the closed-form result.

So the value of Euler's Phi function for the RSA modulus formed from the primes 7 and 11 is 60.