Eulers Totient Function

ɸ(n) = Count of positive integers greater than 0 and less than ‘n’ that are relatively prime to n
i.e. the numbers whose GCD with n is 1

ɸ(5) = {1, 2, 3, 4} = 4
ɸ(6) = {1, 5} = 2

ɸ(n) = n - 1 (When ‘n’ is prime)
ɸ(n) = ɸ(a * b) = ɸ(a) * ɸ(b) = (a - 1) * (b - 1) when a & b are prime numbers
ɸ(n) = $n(1-\frac{1}{p_1})(1-\frac{1}{p_2})$ … (where $p_1,p_2$, … are distinct prime factors of n)

Prime factors : Factors of an number that are themselves prime

ɸ(6) = ɸ(2) * ɸ(3) = (2 -1) * (3 - 1) = 2

ɸ(1000)
n = 1000 = $2^3\ast 5^3$
ɸ(1000) = $1000(1-\frac{1}{2})(1-\frac{1}{5})$
ɸ(1000) = 400