Suppose a store owner has 3664 apples and 1920 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: 3664, 1920
Find GCD(3664 and 1920) = ?
step 2 Find the prime factors of all integers in the group:
3664 = 2 x 2 x 2 x 2 x 229
1920 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5
step 3 Identify the common prime factors:
The common prime factors shared by all integers (3664, 1920) are: 2 × 2 × 2 × 2.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(3664, 1920) = 2 × 2 × 2 × 2 = 16.
step 5 Real-world conclusion:
The maximum number of identical fruit baskets that can be made is 16.
Each basket will contain 229 apples and 120 oranges.
GCD(3664, 1920) = 16
