In order to put bags together of these items with no leftovers, you need to find the Greatest Common Factor (GCF) of each number. Factors are numbers that can be multiplied together to get the number you want (For example, the factors of 10 are 1 and 10, and 2 and 5, or - in numerical order - 1, 2, 5, and 10). The Greatest COMMON Factor is the biggest factor that all three numbers have in common. The GCF will be how many bags you will make. After doing this, you will divide each number by the GCF. Those three numbers (120 divided by the GCG, 75 divided by the GCF, and 30 divided by the GCF) will be how many of each item you have to put in each bag in order to have identical bags with no leftovers. Let's begin:
The factors of 30, in order, are 1, 2, 3, 5, 6, 10, 15, and 30 (1 x 30, 2 x 15, 3 x 10, and 5 x 6).
The factors of 75 , in order, are 1, 3, 5, 15, 25, and 75 (1 x 75, 3 x 25, and 5 x 15).
The factors of 120, in order, are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120 (1 x 120, 2 x 60, 3 x 40, and so on).
If you look closely, you'll see the biggest factor they have in common is 15. This is how many bags you'll have to make. Now divide 30, 75, and 120 by 15 each (30/15, 75/15, and 120/15). 30/15 = 2, 75/15 = 5, and 120/15 = 8.
Therefore, if you have 120 grapes, 75 orange slices, and 30 granola bars, you'll have to make 15 bags. Each bag will have 8 grapes, 5 orange slices, and 2 granola bars. 15 is the GREATEST number of bags you will have to make.
