Find the number of co-primes to the number 144, that are less than the number itself?*1 point48326456

To find the number of co-primes to the number 144 that are less than the number itself, we need to find the Euler's totient function of 144.

The Euler's totient function, φ(n), is used to determine the number of positive integers that are co-prime to n.

Step 1: Prime factorize the number 144. The prime factors of 144 are 2 and 3.

Step 2: Use the formula for Euler's totient function, which is n(1 - 1/p1)(1 - 1/p2)...(1 - 1/pk), where p1, p2, ..., pk are the distinct prime numbers dividing n.

Step 3: Substitute the values into the formula. So, φ(144) = 144(1 - 1/2)(1 - 1/3) = 144 * 1/2 * 2/3 = 48.

So, there are 48 numbers less than 144 that are co-prime to 144.