Question

The length, breadth & height of a room are 840 cm, 600 cm, and 420cm respectively. Find the longest tape which can measure the 3-D of the room exactly?

Answer 1

Given -

• Length of room = 840 cm
• Breadth of room = 600 cm
• Height of room = 420 cm

To find -

• Longest tape to measure length, breadth and height.

Solution -

Prime factorisation of 840 -

$\begin{array}{r | l}2&840\\\cline{2-2}2 & 420 \\\cline{2-2} 2 & 210 \\\cline{2-2} 3 & 105 \\\cline{2-2} 5 & 35 \\\cline{2-2} 7 & 7 \\\cline{2-2} & 1\end{array}$

Prime factorisation of 600 -

$\begin{array}{r | l}2&600 \\\cline{2-2} 2 & 300 \\\cline{2-2} 2 & 150 \\\cline{2-2} 3 &75 \\ \cline{2-2} 5 &25 \\\cline{2-2} 5 &5 \\ \cline{2-2} & 1 \end{array}$

Prime factorisation of 420 -

$\begin{array}{r | l}2 & 420 \\\cline{2-2} 2 & 210 \\\cline{2-2} 3 & 105 \\\cline{2-2} 5 & 35 \\\cline{2-2} 7 & 7 \\\cline{2-2} & 1\end{array}$

___________________________

HCF of room dimensions by prime factorisation -

• 840 = 2³ × 3 × 5 × 7
• 600 = 2³ × 3 × 5²
• 420 = 2² × 3 × 5 × 7

HCF ( 840, 600 & 420 ) = 2² × 3 × 5

= 60 cm

Therefore, the length of longest rod that can measure of three dimensions of the room = 60 cm.