Suppose a store owner has 33333333 apples and 2222222222222222 oranges and wants to package them into identical fruit baskets so that every basket contains an equal number of each item without leaving any remainder. What is the maximum number of identical fruit baskets that can be made, and how many of each item will be in each basket?
GCD Problem and Solution:
step 1 Address the method, input parameters and values:
Integers: 33333333, 2222222222222222
Find GCD(33333333 and 2222222222222222) = ?
step 2 Find the prime factors of all integers in the group:
33333333 = 3 x 11 x 73 x 101 x 137
2222222222222222 = 2 x 11 x 17 x 73 x 101 x 137 x 5882353
step 3 Identify the common prime factors:
The common prime factors shared by all integers (33333333, 2222222222222222) are: 11 × 73 × 101 × 137.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(33333333, 2222222222222222) = 11 × 73 × 101 × 137 = 11111111.
step 5 Real-world conclusion:
The maximum number of identical fruit baskets that can be made is 11111111.
Each basket will contain 3 apples and 200000002 oranges.
GCD(33333333, 2222222222222222) = 11111111
