Suppose a store owner has 1006 apples and 1266 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: 1006, 1266
Find GCD(1006 and 1266) = ?
step 2 Find the prime factors of all integers in the group:
1006 = 2 x 503
1266 = 2 x 3 x 211
step 3 Identify the common prime factors:
The common prime factors shared by all integers (1006, 1266) are: 2.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(1006, 1266) = 2 = 2.
step 5 Real-world conclusion:
The maximum number of identical fruit baskets that can be made is 2.
Each basket will contain 503 apples and 633 oranges.
GCD(1006, 1266) = 2
