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Question

Shannon wants to make snack bags that contain an equal amount of three different types of nuts. If she has 26 almonds, 78 pecans, and 52 peanuts, what will be the most number of bags she can have?

Answer 1

Find the prime factors of each number:

 

    "26 almonds"         26 = 2 * 13

   "78 peanuts"          78 = 2 * 3 * 13

   "56 peanuts"          56 = 2 * 2 * 13

 

The term "equal amount" determines how the above numbers may be used.  For example, Shannon may make 2 * 13 bags (because those number appear in all of the lists).  She will have some left over. 

 

  So, 2*13 = 26 bags, each bag containing one of each of the three kinds of nut  ["equal amounts" in each bag]