Suppose a store owner has 1800 apples and 144000 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: 1800, 144000
Find GCD(1800 and 144000) = ?
step 2 Find the prime factors of all integers in the group:
1800 = 2 x 2 x 2 x 3 x 3 x 5 x 5
144000 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5
step 3 Identify the common prime factors:
The common prime factors shared by all integers (1800, 144000) are: 2 × 2 × 2 × 3 × 3 × 5 × 5.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(1800, 144000) = 2 × 2 × 2 × 3 × 3 × 5 × 5 = 1800.
step 5 Real-world conclusion:
The maximum number of identical fruit baskets that can be made is 1800.
Each basket will contain 1 apples and 80 oranges.
GCD(1800, 144000) = 1800
