Three whole numbers have capacities of 24 litres, 500 litres and 120 litres. What is the volume of the largest container that can be used to fill each of them on exact number of times
To find the volume of the largest container that can be used to fill each of them an exact number of times, we need to find the greatest common divisor (GCD) of the three capacities.
The prime factorization of 24 is 2^3 x 3^1.
The prime factorization of 500 is 2^2 x 5^3.
The prime factorization of 120 is 2^3 x 3^1 x 5^1.
To find the GCD, we need to find the highest power of each prime factor that is common to all three numbers. In this case, the highest power of 2 that is common to all three numbers is 2^2. The highest power of 3 that is common to all three numbers is 3^1. The highest power of 5 that is common to all three numbers is 5^0 (since 5^1 is only in the factorization of 120).
Therefore, the GCD of 24, 500, and 120 is 2^2 x 3^1 = 12.
So, the largest container that can be used to fill each of them an exact number of times has a volume of 12 litres.