Suppose a store owner has 326 apples and 424 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: 326, 424
Find GCD(326 and 424) = ?
step 2 Find the prime factors of all integers in the group:
326 = 2 x 163
424 = 2 x 2 x 2 x 53
step 3 Identify the common prime factors:
The common prime factors shared by all integers (326, 424) are: 2.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(326, 424) = 2 = 2.
step 5 Real-world conclusion:
The maximum number of identical fruit baskets that can be made is 2.
Each basket will contain 163 apples and 212 oranges.
GCD(326, 424) = 2
