Suppose a store owner has 217 apples and 285 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: 217, 285
Find GCD(217 and 285) = ?
step 2 Find the prime factors of all integers in the group:
217 = 7 x 31
285 = 3 x 5 x 19
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(217, 285) = 1.
step 5 Real-world conclusion:
Since the GCD is 1, only 1 single basket containing all items (217 apples and 285 oranges) can be made without dividing them further.
GCD(217, 285) = 1
