Question

Claire bought 180 candies and 140 pens for goody bags for her birthday. What is the largest number of goody bags that Claire can make so that each goody bag has the same number of candies and the same number of pens?

Answer 1

Wouldn't it be 140 bags with one of each in it; unless you need to use all the candies?

Answer 2

Answer: 20

Explanation:

Given : Claire bought 180 candies and 140 pens for goody bags for her birthday.

To find : The largest number of goody bags that Claire can make so that each goody bag has the same number of candies and the same number of pens ( such that no pens or candies left).

So we find the GCF ( Greatest common factor ) or Number of candies and Number of pens.

i.e. we need to find GCF of 180 and 140 .

Prime factorization of 180 =
`2*2*3*3*5`

Prime factorization of 140 =
`2*2*7*5`

The greatest common factor of 180 & 140 =
`2*2*5=20`

∴ Claire can make 20 goody bags so that each goody bag has the same number of candies and the same number of pens.