Question

The length and breadth of a rectangular field is 110 m and 30 m respectively. Calculate the length of the longest rod which can measure the length and breath of the field exactly.

Answer 1

Given that the length and breadth of a rectangular field is $110$ m and $30$ m respectively.

The length of the longest rod that can measure both the length and breadth of the field exactly will be the highest common factor $\left(HCF\right)$ of the length and breadth.

Therefore, factorise $110$ as follows:

$110=2\times 5\times 11$

Now, factorise $30$ as follows:

$30=2\times 3\times 5$

We know that $HCF$ is the highest common factor.

Since the common factor between the numbers $110$ and $30$ is $2\times 5=10$.

Hence, the length of the longest rod which can measure the length and breadth of the field exactly, is $10m$