Suppose a store owner has 5180 apples and 2598990 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: 5180, 2598990
Find GCD(5180 and 2598990) = ?
step 2 Find the prime factors of all integers in the group:
5180 = 2 x 2 x 5 x 7 x 37
2598990 = 2 x 3 x 5 x 41 x 2113
step 3 Identify the common prime factors:
The common prime factors shared by all integers (5180, 2598990) are: 2 × 5.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(5180, 2598990) = 2 × 5 = 10.
step 5 Real-world conclusion:
The maximum number of identical fruit baskets that can be made is 10.
Each basket will contain 518 apples and 259899 oranges.
GCD(5180, 2598990) = 10
