The greatest number of packages of baked items that can be sold is 10
Solution:
Given that there are 50 cupcakes and 160 cookies to be sold at the school bake sale
To find: greatest number of packages of baked items that can be sold
Each package has the same number of cupcakes and same number of cookies with none left over
So, we have to find the greatest common factor of 50 and 160
The greatest number that is a factor of two (or more) other numbers.
When we find all the factors of two or more numbers, and some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor.
Greatest common factor of 50 and 160:
The factors of 50 are: 1, 2, 5, 10, 25, 50
The factors of 160 are: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
Then the greatest common factor is 10
So the greatest number of packages sold is 10
Each package will contain:
Given that there 50 cupcakes and 160 cookies
Number of cupcakes in 1 package:
Number of cookies in 1 package:
So each package has the same number of cupcakes and same number of cookies with none left over