The length and breadth of our school hall are 2000 cm and 1600 cm. Let's find the length of the longest tape which can measure both length and breadth in exact whole numbers?
Answer (1)
To find the length of the longest tape that can measure both the length and the breadth of the school hall in exact whole numbers, we need to find the greatest common divisor (GCD) of the two dimensions.
The length of the hall is 2000 cm and the breadth is 1600 cm.
Here are the steps to find the GCD:
List the factors of each number:
Factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000.
Factors of 1600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, 1600.
Identify the common factors :
Common factors are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400.
Choose the greatest common factor , which is the GCD:
The greatest common factor is 400.
Therefore, the length of the longest tape that can measure both the length and the breadth of the hall in exact whole numbers is 400 cm.
