Suppose a store owner has 137 apples and 261 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: 137, 261
Find GCD(137 and 261) = ?
step 2 Find the prime factors of all integers in the group:
137 = 137
261 = 3 x 3 x 29
step 3 Identify the common prime factors:
There are no common prime factors (other than 1) between the integers.
step 4 Calculate the greatest common factor:
Therefore, GCD(137, 261) = 1.
step 5 Real-world conclusion:
Since the GCD is 1, only 1 single basket containing all items (137 apples and 261 oranges) can be made without dividing them further.
GCD(137, 261) = 1
