Suppose a store owner has 9900 apples and 34664 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: 9900, 34664
Find GCD(9900 and 34664) = ?
step 2 Find the prime factors of all integers in the group:
9900 = 2 x 2 x 3 x 3 x 5 x 5 x 11
34664 = 2 x 2 x 2 x 7 x 619
step 3 Identify the common prime factors:
The common prime factors shared by all integers (9900, 34664) are: 2 × 2.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(9900, 34664) = 2 × 2 = 4.
step 5 Real-world conclusion:
The maximum number of identical fruit baskets that can be made is 4.
Each basket will contain 2475 apples and 8666 oranges.
GCD(9900, 34664) = 4
