Suppose a store owner has 444444444444 apples and 10000000000 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: 444444444444, 10000000000
Find GCD(444444444444 and 10000000000) = ?
step 2 Find the prime factors of all integers in the group:
444444444444 = 2 x 2 x 3 x 7 x 11 x 13 x 37 x 101 x 9901
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
step 3 Identify the common prime factors:
The common prime factors shared by all integers (444444444444, 10000000000) are: 2 × 2.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(444444444444, 10000000000) = 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 111111111111 apples and 2500000000 oranges.
GCD(444444444444, 10000000000) = 4
