Question

The length, breadth and height of a room are 12m, 15m and 18m respectively. Determine the longest tape which can measure all the three dimensions of the room exactly.

Answer 1

Hint: To determine the longest tape that can measure all the three dimensions of the room exactly, there needs to be a tape whose length is a common factor of the dimensions of the room. And to find a common factor which is the greatest, we need to find the H.C.F. of the three dimensions.

Complete step by step solution:
To measure the dimensions of a room exactly, there needs to be a tape whose length should not exceed or come short of the value of the exact dimension. Thus, the length of the tape needs to be a common factor of the values of the three dimensions of the room.
Now, it is given that,
Length of the room = 12m
Breadth of the room = 15m
 Height of the room = 18m
Now to find the length of the longest tape that can measure all the three dimensions of the room exactly, we need to find the highest common factor (or H.C.F.) of 12, 15 and 18.
The three numbers can be factored as:
$\begin{align}
  & 12=2\times 2\times 3={{2}^{2}}\times 3 \\
 & 15=3\times 5 \\
 & 18=2\times 3\times 3=2\times {{3}^{2}} \\
\end{align}$
Thus, the highest common factor (H.C.F.) of the three dimensions is 3.
Hence, the longest tape that can measure the three dimensions of the room exactly is of length 3m.

Note: The H.C.F. of 12, 15 and 18 can be alternatively found without factoring by using a long division method. From where we can find the common factor of all 3 numbers.