Suppose a store owner has 2590018 apples and 2598960 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: 2590018, 2598960
Find GCD(2590018 and 2598960) = ?
step 2 Find the prime factors of all integers in the group:
2590018 = 2 x 17 x 17 x 4481
2598960 = 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7 x 13 x 17
step 3 Identify the common prime factors:
The common prime factors shared by all integers (2590018, 2598960) are: 2 × 17.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(2590018, 2598960) = 2 × 17 = 34.
step 5 Real-world conclusion:
The maximum number of identical fruit baskets that can be made is 34.
Each basket will contain 76177 apples and 76440 oranges.
GCD(2590018, 2598960) = 34
