Greatest Common Divisor (GCD)

To find the greatest number that will divide 24, 36, and 120 without leaving any remainder, we need to find the greatest common divisor (GCD) of these numbers. The GCD is the largest number that divides all the given numbers evenly.

Prime Factorization

To find the GCD, we first need to prime factorize the given numbers. Prime factorization is the process of expressing a number as a product of its prime factors.

Let's prime factorize the given numbers:

- 24 = 2 x 2 x 2 x 3
- 36 = 2 x 2 x 3 x 3
- 120 = 2 x 2 x 2 x 3 x 5

Finding Common Factors

Now, we need to identify the common factors in the prime factorizations of the given numbers. These common factors will be the prime factors that are present in all the numbers.

Common factors of 24, 36, and 120:

- 2 x 2 x 3 = 12

Greatest Common Divisor (GCD)

The greatest common divisor (GCD) of 24, 36, and 120 is 12. This means that 12 is the largest number that divides all the given numbers without leaving any remainder.

Therefore, the greatest number that will divide 24, 36, and 120 without leaving any remainder is 12.