Greatest Common Factor

Question

Of the 108 students in the school band, 48 are in the woodwind section, 24 are in thr percussion section, and 36 are in the brass section.  How many woodwind players, percusion players, and brass players will there be in each group?

Answer 1

Cecilia, how do we find the greatest common factor??

 

Do a factor tree for all three numbers. What matches up between all three is multiplied together to give you your GCF. What's left over in each is your answer.

Answer 2

Hello Cecilia,

To answer this question, we need one more piece of information. Let us say that the band leader wants to divide the band into as many equal groups as possible.  In that case we want to find the greatest common factor of the three numbers, 48, 24 and 36. All three numbers are divisible by 2, 3, 4, 6, and 12. No number greater than 12 divides evenly into all three numbers. Therefore the greatest common factor is 12. If we specify the number of groups as 12,

we can put 4 woodwind players, 2 percussion players, and 3 brass players into each group.

 Does this help? That is, were you able to follow this logic, to see how attempting to find the greatest common factor required me to come up with that particular additional piece of information? I hope so.

 

 

Answer 3

9X12 = 108

4X12 = 48

2X12 = 24

3X12=36

 

12 is the gcf :)