Determining Equal Sharing Using Factors

Our problem yesterday was to determine the maximum number of snack packs that could be made with 2 or 3 different items.  First we used 24 apples and 36 bags of trail mix.  We have to find out the common factors first.  We did this by making a Venn diagram (we have used these before).

As you can see, 1, 2, 3, 4, 6, and 12 are the common factors of 24 and 36.  So:

Packs                       Apples                              Bags of Trail Mix

1                                        24                                             36

2                                        12                                             18

3                                         8                                              12

4                                         6                                               9

6                                         4                                               6

12                                       2                                               3

We use fact families to determine this, but we usually do this in our heads by now.  It would look like this:

1x24=24                      1x36=36

2x12=24                      2x18=36

3x8 = 24                      3x12=36

4x6 = 24                      4x9  =36

6x4 = 24                      6x6  =36

12x2=24                     12x3=36

The ones in bold are the ones that are common factors and the number of packs we can have so we use the other number of the factor pair to determine what amount of apples and trail mix can go in each pack.