Suppose a store owner has 1000 apples and 1668 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: 1000, 1668
Find GCD(1000 and 1668) = ?
step 2 Find the prime factors of all integers in the group:
1000 = 2 x 2 x 2 x 5 x 5 x 5
1668 = 2 x 2 x 3 x 139
step 3 Identify the common prime factors:
The common prime factors shared by all integers (1000, 1668) are: 2 × 2.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(1000, 1668) = 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 250 apples and 417 oranges.
GCD(1000, 1668) = 4
