Suppose a store owner has 1140510 apples and 440 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: 1140510, 440
Find GCD(1140510 and 440) = ?
step 2 Find the prime factors of all integers in the group:
1140510 = 2 x 3 x 5 x 7 x 5431
440 = 2 x 2 x 2 x 5 x 11
step 3 Identify the common prime factors:
The common prime factors shared by all integers (1140510, 440) are: 2 × 5.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(1140510, 440) = 2 × 5 = 10.
step 5 Real-world conclusion:
The maximum number of identical fruit baskets that can be made is 10.
Each basket will contain 114051 apples and 44 oranges.
GCD(1140510, 440) = 10
