Question

the Length breadth and height of a room are 168 centimetre 105 cm and 231 CM respectively find the length of the longest tape which can measure the dimensions of the room exactly​

Answer 1

In this question, We will find the HCF (Highest Common Factor) of the dimensions given above.

Given,

Length = 168 cm = 2 x2 x 2 x 3 x 7

Breadth = 105 cm = 7 x 3 x 5

Height = 231 cm = 3 x 7 x 11


Since, In the data we find that 3 and 7 are the Highest Common Factors.


Length of Longest Tape = HCF

=> Length of Longest Tape = (3 x 7) cm

=> Length of longest tape = 21 cm

Answer 2

Answer :

The length of longest tape which can measure the dimensions of the room exactly is 21 cm.

Step-by-step explanation :

Given,

Length of room = 168 cm

Breadth of room = 105 cm

Height of room = 231 cm

To find - The length of longest tape which can measure the dimensions of the room exactly.

So, in order to find the length of longest tape which can measure the dimensions of the room exactly, we need to find the HCF of the three.

By Prime factorisation method

⇒ 168

$\begin{array}{r | l}2 & 168\\ \cline{2-2}2 & 84\\ \cline{2-2}2 & 42\\ \cline{2-2}3 & 21\\ \cline{2-2}7 & 7\\ \cline{2-2} & 1\end{array}$

⇒ 105

$\begin{array}{r | l}3 & 105\\ \cline{2-2}5 & 35\\ \cline{2-2}7 & 7\\ \cline{2-2} & 1\end{array}$

⇒ 231

$\begin{array}{r | l}3 & 231\\ \cline{2-2}7 & 77\\ \cline{2-2}11 & 11\\ \cline{2-2} & 1\end{array}$

168 = 2 × 2 × 2 × 3 × 7

105 = 3 × 5 × 7

231 = 3 × 7 × 11

So, common terms in all three are 3 and 7.

Therefore, the HCF of 168, 105 and 231 -

⇒ 3 × 7

⇒ 21