Martha's mom is making party bags for all of her guests. She has 24 green gumballs and 33 blue gumballs. If she splits them evenly between all the bags without any leftovers, how many bags can she make?

3 bags

Step-by-step explanation:

Suppose there are  

x

bags of candy.

If the  

33

blue gumballs are to be split evenly with no leftovers among the  

x

bags, then  

x

must divide evenly into  

33

.

If the  

24

green gumballs are to be split evenly with no leftovers among the  

x

bags, then  

x

must divide evenly into  

24

.

To get the largest number of bags (

x

),

x

must be the Greatest Common Divisor of  

33

and  

24

Factoring:

33

=  

3

×

8

24

=  

2

×

2

×

2

×

3

The only common factor is  

3

and therefore the product of the common factors is  

3

or, in other words,

the Greatest Common Factor is  

x

=

3