An architect is designing a house in which a 104 square foot room and a 130 square foot room share a wall. What is the greatest possible integer length of the shared wall?
Is it the greatest common factor?
well,
104 = 2^3 * 13
130 = 2 * 5 * 13
so, find the GCD.
Yes, to find the greatest possible integer length of the shared wall, we can consider finding the greatest common factor (GCF) of the two room sizes. The GCF represents the largest number that can evenly divide both room sizes.
First, let's find the factors of each room size:
Factors of 104: 1, 2, 4, 8, 13, 26, 52, 104
Factors of 130: 1, 2, 5, 10, 13, 26, 65, 130
There are multiple common factors between 104 and 130, but the greatest common factor is 26. Therefore, the greatest possible integer length of the shared wall is 26 feet.
Yes, to find the greatest possible integer length of the shared wall, we need to find the greatest common factor (GCF) between the areas of the two rooms. The GCF represents the largest number that can evenly divide both room areas.
In this case, the areas of the two rooms are 104 square feet and 130 square feet. To find the GCF, we can list the factors of each number and identify the largest common factor they share.
Factors of 104: 1, 2, 4, 8, 13, 26, 52, 104
Factors of 130: 1, 2, 5, 10, 13, 26, 65, 130
Looking at the lists, we can see that the largest common factor is 26. Therefore, the greatest possible integer length of the shared wall between the two rooms is 26 feet.