Suppose a store owner has 87654 apples and 3456789 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: 87654, 3456789
Find GCD(87654 and 3456789) = ?
step 2 Find the prime factors of all integers in the group:
87654 = 2 x 3 x 7 x 2087
3456789 = 3 x 7 x 97 x 1697
step 3 Identify the common prime factors:
The common prime factors shared by all integers (87654, 3456789) are: 3 × 7.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(87654, 3456789) = 3 × 7 = 21.
step 5 Real-world conclusion:
The maximum number of identical fruit baskets that can be made is 21.
Each basket will contain 4174 apples and 164609 oranges.
GCD(87654, 3456789) = 21
