How many natural numbers 252 are relatively prime to 252Solu

How many natural numbers 252 are relatively prime to 252?

A number that is relatively prime to another number means that the GCD of the two numbers is 1.

Method for calculating the number of relatively prime numbers less than a given number involves prime factorization

1. Find the exponential prime factorization of the number.

2. Taking each term separately, change the term to 2 numbers:

a. Subtract 1 from the base for the first number.

b. Subtract 1 from the exponent and evaluate the expression for the second number. (If the exponent is 1, the second number is always 1.)

3. Multiply all the numbers together found in step 2

The prime factorization of 252 is: 2² x 3² x 7.

b. Taking 2² first, we get: 2 - 1 = 1 and 2^2-1 = 2.

c. Taking 3² we get: 3 - 1 = 2 and 3^2-1 = 3

d. Taking 7¹ we get 7-1 = 6 and 7^{1-1 =} 1

d. Multiplying all of them together we get: (1)(2)(2)(3)(6)(1) .

e. The answer is 72.