Albert has 18 blue marbles and 20 white ones. If he wants to place them in identical groups without any marbles left over, what is the greatest number of groups Albert can make?
15
GCF(18,20) = 2.
So, at most 2 groups can be made.
To find the greatest number of groups Albert can make with the given marbles, we need to find the greatest common divisor (GCD) of 18 and 20. The GCD will represent the largest number of groups without any marbles left over.
To find the GCD, we can use the Euclidean algorithm:
Step 1: Divide 20 by 18. The remainder is 2.
Step 2: Divide 18 by 2. The remainder is 0.
Since the remainder is 0, we can conclude that the GCD of 18 and 20 is 2.
Therefore, Albert can make a maximum of 2 groups with the marbles without any marbles left over.