Rey need alex and taylor are in separate rooms. alex has 24 coins and taylor has 18 coins. each person knows how many coins the other has. each boy is to put his coins into groups with the same number of coins in them. they will win the grand prize if the number of groups alex has matches the number of groups taylor has. what is the greatest number of groups alex could make and still have a chance at winning the grand prize?

If you think about it, the question is asking us to find the greatest common factor, or GCF, of the two numbers, 24 and 18. 
First, find all of the factors of 24. 
The factors are: 1, 2, 3, 4, 6, 8, 12, 24 
Next, find the factors of 18.
The factors are: 1, 2, 3, 6, 9, 18 
List out all of the factors that both of the numbers have. 
The factors are: 1, 2, 3, 6
Whichever is the greatest of these numbers is the GCF. 
The GCF is 6, so the greatest number of groups he can make and still be able to win is 6. 
Hope this helps!