Name: Questions on HCF
Uploaded: 2019-07-19
Duration: 16 min 56 s
Description: In this video, we will cover the definition, properties and different types methods used to find out the Highest common factor (HCF). This video will be help...

Question

A rectangular courtyard is

18 m 72 cm

long and

13 m 20 cm

broad. It is to be paved with square tiles of the same size. Find the least number of such tiles.

Accepted Answer

Given that a rectangular courtyard is $18 m 72 cm$ long and $13 m 20 cm$ broad. It is to be paved with square tiles of the same size.

We need to find the least number of such tiles.

Since, we require square tiles, the length of the side of the square tile has to be found out. The length of the square tile will be the $HCF$ of the given measure of sides.

We know that $1 m = 100 cm$

$\Rightarrow 18 m = 1800 cm$

$\Rightarrow$ Length $= 18 m 72 cm = 1800 cm + 72 cm = 1872 cm$

Similarly, breadth $= 13 m 20 cm = 1300 cm + 20 cm = 1320 cm$

Now, can find the $HCF$ between $1872$ and $1320$ by division method.

The division is carried out by considering the remainder of first step as the divisor of the second step and the divisor of the first step as the dividend for the second step. This process is continued, until a zero remainder is obtained.

We know that the $HCF$ of the numbers will be the last divisor for which the remainder is $0$ in the division.

The remainder is $0$ when the divisor is $24$ .

So, the $HCF of 1872 and 1320 = 24$

Hence, the length of each tile $= 24 cm$

Now, we need to find the number of square tiles required to pave the courtyard.

Number of tiles required to pave the courtyard

$= \frac{Area of the rectangular courtyard}{Area of each tile}$

$= \frac{length \times breadth}{side \times side}$

$= \frac{1872 cm \times 1320 cm}{24 cm \times 24 cm}$

$= \frac{1872 \times 1320}{24 \times 24}$

$= 78 \times 55$

$= 4290$

Hence, $4290$ square tiles are required to pave the courtyard.

A rectangular courtyard is $18 m 72 cm$ long and $13 m 20 cm$ broad. It is to be paved with square tiles of the same size. Find the least number of such tiles.

Important Questions on Factors and Multiples

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