Suppose a store owner has 944 apples and 368 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: 944, 368
Find GCD(944 and 368) = ?
step 2 Find the prime factors of all integers in the group:
944 = 2 x 2 x 2 x 2 x 59
368 = 2 x 2 x 2 x 2 x 23
step 3 Identify the common prime factors:
The common prime factors shared by all integers (944, 368) are: 2 × 2 × 2 × 2.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(944, 368) = 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 59 apples and 23 oranges.
GCD(944, 368) = 16
