Suppose a store owner has 9468 apples and 12264 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: 9468, 12264
Find GCD(9468 and 12264) = ?
step 2 Find the prime factors of all integers in the group:
9468 = 2 x 2 x 3 x 3 x 263
12264 = 2 x 2 x 2 x 3 x 7 x 73
step 3 Identify the common prime factors:
The common prime factors shared by all integers (9468, 12264) are: 2 × 2 × 3.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(9468, 12264) = 2 × 2 × 3 = 12.
step 5 Real-world conclusion:
The maximum number of identical fruit baskets that can be made is 12.
Each basket will contain 789 apples and 1022 oranges.
GCD(9468, 12264) = 12
