Suppose a store owner has 190790 apples and 34567890 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: 190790, 34567890
Find GCD(190790 and 34567890) = ?
step 2 Find the prime factors of all integers in the group:
190790 = 2 x 5 x 19079
34567890 = 2 x 3 x 5 x 7 x 97 x 1697
step 3 Identify the common prime factors:
The common prime factors shared by all integers (190790, 34567890) are: 2 × 5.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(190790, 34567890) = 2 × 5 = 10.
step 5 Real-world conclusion:
The maximum number of identical fruit baskets that can be made is 10.
Each basket will contain 19079 apples and 3456789 oranges.
GCD(190790, 34567890) = 10
