Suppose a store owner has 23 apples and 287 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: 23, 287
Find GCD(23 and 287) = ?
step 2 Find the prime factors of all integers in the group:
23 = 23
287 = 7 x 41
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(23, 287) = 1.
step 5 Real-world conclusion:
Since the GCD is 1, only 1 single basket containing all items (23 apples and 287 oranges) can be made without dividing them further.
GCD(23, 287) = 1
