Suppose a store owner has 7890625 apples and 3906250 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: 7890625, 3906250
Find GCD(7890625 and 3906250) = ?
step 2 Find the prime factors of all integers in the group:
7890625 = 5 x 5 x 5 x 5 x 5 x 5 x 5 x 101
3906250 = 2 x 5 x 5 x 5 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 (7890625, 3906250) are: 5 × 5 × 5 × 5 × 5 × 5 × 5.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(7890625, 3906250) = 5 × 5 × 5 × 5 × 5 × 5 × 5 = 78125.
step 5 Real-world conclusion:
The maximum number of identical fruit baskets that can be made is 78125.
Each basket will contain 101 apples and 50 oranges.
GCD(7890625, 3906250) = 78125
