Question

8. The length, breadth and height of a room are 768 cm, 576 cm and 832 cm respective longest tape which can measure the three dimensions of the room exactly. 5​

Answer 1

$\large\text{\underline{Required}}$

The longest tape which can measure the length, breadth, and height of $768\text{ cm}$, $576\text{ cm}$, and $832\text{ cm}$.

$\large\text{\underline{Solution}}$

Here is some information about what is the highest common factor.

$\large\red{\bigstar}\blue{\text{\underline{The HCF}}}$

The tape can measure the length exactly if it exactly divides the three dimensions. In this case, such a number is called the HCF of three numbers, and it divides without any remainder, while being the greatest possible number.

So the answer requires the HCF of three numbers $768$, $576$, and $832$.

We can find the HCF using the successive division method.

$\large\red{\bigstar}\blue{\text{\underline{HCF using successive division}}}$

Step 1: Choose one number that divides all numbers.

Step 2: Divide each by the number.

Step 3: When they are no longer divisible, the product of the number which divided the number becomes the HCF.

$\large\text{\underline{Required answer}}$

$64\text{ cm}$ is the longest length of tape that can exactly measure the three dimensions.

Answer 2

Given :-

Length = 768 cm

Breadth = 576 cm

Height = 832 cm

To Find :-

Length of longest tape

Solution :-

By prime factorization method

2 | 768

2 | 384

2 | 192

2 | 96

2 | 48

2 | 24

2 | 12

2 | 6

3 | 1

768 = 2⁸ × 1

576

576

2 | 288

2 | 144

2 | 72

2 | 36

2 | 18

2 | 9

3 | 3

3 | 1

576 = 2⁶ × 3²

832

2 | 416

2 | 208

2 | 104

2 | 52

2 | 26

2 | 13

13 | 1

832 = 2⁶ × 13

Common factor = 2⁶

HCF = 2⁶

HCF = 64

Length of longest tape = 64 m