A room measures 540cm by 420cm find the length of the largest square tiles that can be used to cover the floor with out requiring any cutting ?
540 = 2^2 3^3 5^1
420 = 2^2 3^1 5^1 7^1
2^2 = 4 is the only common square factor, so use
135 by 105 tiles, each 2x2
What is the answer left in powers
Well, let's imagine we have some gigantic square tiles. We need to find the largest square tile that can fit without requiring any cutting.
To do that, we need to find the greatest common divisor (GCD) of the two dimensions of the room, which are 540 and 420.
Now, the GCD of 540 and 420 is like the superhero who saves the day by dividing both numbers perfectly. And the GCD of 540 and 420 is... *drumroll*... 60!
So the largest square tile that could be used to cover the floor without requiring any cutting would be a 60cm by 60cm tile. Now, if only we had a magical tile enlarger that could transform it into a gigantic clown-sized tile. That would be quite a sight!
To find the length of the largest square tiles that can be used to cover the floor without requiring any cutting, we need to find the greatest common divisor (GCD) of the length and width of the room.
The GCD of 540 and 420 can be found by using the Euclidean algorithm.
Step 1: Divide 540 by 420
540 ÷ 420 = 1 remainder 120
Step 2: Divide 420 by 120
420 ÷ 120 = 3 remainder 60
Step 3: Divide 120 by 60
120 ÷ 60 = 2 remainder 0
Since we have a remainder of 0, the GCD of 540 and 420 is 60.
Therefore, the length of the largest square tiles that can be used to cover the floor without requiring any cutting is 60 cm.
To find the length of the largest square tiles that can be used to cover the floor without requiring any cutting, we need to find the greatest common divisor (GCD) of the two given dimensions (540cm and 420cm).
Step 1: Find the GCD of 540 and 420.
One way to find the GCD is by using the prime factorization method:
Prime factorization of 540:
540 = 2² × 3³ × 5¹
Prime factorization of 420:
420 = 2² × 3¹ × 5¹ × 7¹
Now, we need to find the common prime factors of both numbers:
The common prime factors are 2² and 3¹.
Step 2: Multiply the common prime factors.
2² × 3¹ = 4 × 3 = 12
The greatest common divisor (GCD) of 540 and 420 is 12.
So, the length of the largest square tiles that can be used to cover the floor without requiring any cutting is 12 cm.