What is the greatest number ?

Question

Mia works for a charity. She has to pack 120 shirts and 84 dresses into bags.

All bags must also contain an equal number of dresses. All items must be packed.

What is the greatest number of bags Mia can make?

Answer 1

Now if all bags must contain an equal number of dresses but not necessarily equal number of shirts, the max number of bags will be 84 as one can put single dress in each bag and no conditions on the number of shirts.

 

But if all the bags should contain an equal number of shirts and dresses both we will do the following.

 

The number of possible dresses in each bag = 1,2,3,4,6,7,12,14,21,27,42,64 (all are factors of 84)

The possible number of bags for each of the above scenario = 84/1,84/2,84/3,84/4,84/6,84/7,84/12,84/14,84/21,84/27,84/42,84/84 = 84,42,27,21,14,12,7,6,4,3,2,1

 

Similarly, the number of possible shirts in each bag = 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120 (factors of 120)

The possible number of bags for each of the above scenario = 120,60,40,30,24,20,15,12,10,8,6,5,4,3,2,1

 

So our answer would be the biggest common factor of 84 and 120.

The common factor of 84 and 120 as we can see are 1,2,3,4,6 and 12. The biggest is 12.

 

So the greatest number of bag Mia can have is 12 with each bag having 10 shirts and 7 dresses

 

 

 

Answer 2

A classical question asking for the Greatest Common Divisor.

 

120 = 2 * 2 * 2 * 3 * 5

84 = 2 * 2 * 3 * 7

 

Greatest Common Multiple = 2 * 2 * 3 = 12

 

Each bag contains 10 shirts and 7 dresses.