College Math Placement Practice Test 2026 – Comprehensive All-in-One Guide for Exam Success!

To find the greatest common divisor (GCD) of 24 and 36, we can start by determining the prime factorizations of each number.

The prime factorization of 24 is:

- 24 = 2 × 2 × 2 × 3 = \(2^3 \times 3^1\)

The prime factorization of 36 is:

- 36 = 2 × 2 × 3 × 3 = \(2^2 \times 3^2\)

Next, in order to find the GCD, we take the lowest power of each common prime factor.

The common prime factors of 24 and 36 are:

- For the prime number 2, the lowest power between \(2^3\) and \(2^2\) is \(2^2\).

- For the prime number 3, the lowest power between \(3^1\) and \(3^2\) is \(3^1\).

Thus, the GCD can be calculated as:

GCD = \(2^2 \times 3^1 = 4 \times 3 = 12\).

Therefore, the greatest common divisor of 24 and 36