Suppose a store owner has 10000000000 apples and 444444444444 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: 10000000000, 444444444444
Find GCD(10000000000 and 444444444444) = ?
step 2 Find the prime factors of all integers in the group:
10000000000 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5
444444444444 = 2 x 2 x 3 x 7 x 11 x 13 x 37 x 101 x 9901
step 3 Identify the common prime factors:
The common prime factors shared by all integers (10000000000, 444444444444) are: 2 × 2.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(10000000000, 444444444444) = 2 × 2 = 4.
step 5 Real-world conclusion:
The maximum number of identical fruit baskets that can be made is 4.
Each basket will contain 2500000000 apples and 111111111111 oranges.
GCD(10000000000, 444444444444) = 4
