GCD of 456 and 105

What is GCD of 456 and 105?
GCD(456, 105) = 3
3 is the greatest common factor of 456 and 105.
3 is the highest common factor or the largest positive integer that divides each one of the integer in this group of 456 and 105.

Suppose a store owner has 456 apples and 105 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: 456, 105
Find GCD(456 and 105) = ?

step 2 Find the prime factors of all integers in the group:
456 = 2 x 2 x 2 x 3 x 19
105 = 3 x 5 x 7

step 3 Identify the common prime factors:
The common prime factors shared by all integers (456, 105) are: 3.

step 4 Multiply the common prime factors to find the greatest common factor:
GCD(456, 105) = 3 = 3.

step 5 Real-world conclusion:
The maximum number of identical fruit baskets that can be made is 3.
Each basket will contain 152 apples and 35 oranges.

GCD(456, 105) = 3