Question:
A store sells bottles of juice is equal size boxes. Garth bought 18 boxes, Rico bought 36 boxes and Mia bought 45 boxes. What is the greatest number of bottles in each box ? How many boxes did each person buy if each box contained the greatest number of bottles?
Answer:
The greatest number of bottles in each box is 9
Garth bought 2 boxes , Rico bought 4 boxes and Mai bought 5 boxes
Solution:
Given that,
Garth bought 18 bottles, Rico bought 36 bottles, and Mai bought 45 bottles
To find, the greatest number of bottles in each box, we have to find the greatest common factor of 18, 36 and 45
G.C.F of 18, 36 and 45:
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.
The factors of 18 are: 1, 2, 3, 6, 9, 18
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 45 are: 1, 3, 5, 9, 15, 45
Then the greatest common factor is 9
Thus, the greatest number of bottles in each box is 9
How many boxes did each person buy if each box contained the greatest number of bottles?
Number of boxes bought by Garth:
Number of bottles bought by Garth = 18
Number of boxes bought by Rico:
Number of bottles bought by Rico = 36
Number of boxes bought by Mai:
Number of bottles bought by Mai = 45
Thus number of boxes bought by each person is found