Suppose a store owner has 234468468234 apples and 432864864432 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: 234468468234, 432864864432
Find GCD(234468468234 and 432864864432) = ?
step 2 Find the prime factors of all integers in the group:
234468468234 = 2 x 3 x 3 x 3 x 7 x 11 x 13 x 13 x 333667
432864864432 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 7 x 11 x 13 x 333667
step 3 Identify the common prime factors:
The common prime factors shared by all integers (234468468234, 432864864432) are: 2 × 3 × 3 × 3 × 7 × 11 × 13 × 333667.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(234468468234, 432864864432) = 2 × 3 × 3 × 3 × 7 × 11 × 13 × 333667 = 18036036018.
step 5 Real-world conclusion:
The maximum number of identical fruit baskets that can be made is 18036036018.
Each basket will contain 13 apples and 24 oranges.
GCD(234468468234, 432864864432) = 18036036018
