Final answer:
To find the greatest integer divisible by two numbers, use the concept of the greatest common divisor (GCD) by using the Euclidean algorithm.
Step-by-step explanation:
To find the greatest integer divisible by two numbers, we can use the concept of the greatest common divisor (GCD). The GCD of two numbers is the largest number that divides both of them without leaving a remainder.
In this case, the GCD of 1800 and 720 can be found using the Euclidean algorithm. We start by dividing the larger number (1800) by the smaller number (720) and finding the remainder. Then, we divide the smaller number by the remainder and find the new remainder. We repeat this process until the remainder becomes zero.
The GCD of 1800 and 720 is 360, which is our answer. Therefore, the greatest integer divisible by 1800 and 720 is 360.