Suppose a store owner has 33750 apples and 421875 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: 33750, 421875
Find GCD(33750 and 421875) = ?
step 2 Find the prime factors of all integers in the group:
33750 = 2 x 3 x 3 x 3 x 5 x 5 x 5 x 5
421875 = 3 x 3 x 3 x 5 x 5 x 5 x 5 x 5 x 5
step 3 Identify the common prime factors:
The common prime factors shared by all integers (33750, 421875) are: 3 × 3 × 3 × 5 × 5 × 5 × 5.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(33750, 421875) = 3 × 3 × 3 × 5 × 5 × 5 × 5 = 16875.
step 5 Real-world conclusion:
The maximum number of identical fruit baskets that can be made is 16875.
Each basket will contain 2 apples and 25 oranges.
GCD(33750, 421875) = 16875
