The length of a floor is 3 m 30 cm and the breadth is 4 m 44 cm. what is the maximum length of square tiles that can completely cover the floor ?
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The length of a floor is 3 m 30 cm and the breadth is 4 m 44 cm. what is the maximum length of square tiles that can completely cover the floor ?
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Answer:
Solution:
Length of floor = 4 m 44 cm = [ (4 * 100) + 44] cm = 444 cm
Breadth of floor = 3 m 30 cm = [ (3 * 100) +
30] cm = 330 cm
GCD(Greatest Common Divisor) means to take out the highest common divisor of two positive integers.
Now, we will take Greatest Common
Divisor of both numbers,
444 = 2*2*3* 37
330 = 2 * 3 * 5 * 11
GCD of 444 and 330 = 2*3=6 We took those factors which were common in both and multiplied.
Maximum Length of the square tile =>
Greatest number which divides both length and breadth of floor i.e. GCD of 444 and 330
Maximum Length of the square tile => 6cm
The maximum length of square tiles that can completely cover the floor is 6 cm.
Answer:
The length of a floor is 3 m 30 cm and the breadth is 4 m 44 cm. what is the maximum length of square tiles that can completely cover the floor ?