Suppose a store owner has 1684 apples and 10000 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: 1684, 10000
Find GCD(1684 and 10000) = ?
step 2 Find the prime factors of all integers in the group:
1684 = 2 x 2 x 421
10000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5
step 3 Identify the common prime factors:
The common prime factors shared by all integers (1684, 10000) are: 2 × 2.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(1684, 10000) = 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 421 apples and 2500 oranges.
GCD(1684, 10000) = 4
