Question

What is the minimum number of identical square tiles required to completely cover a floor of dimensions $8m70cm$ by $6m38cm$?

• A. $143$
• B. $165$
• C. $187$
• D. $209$

Answer 1

Answer: (B)

$165$

We first need to calculate HCF of the dimensions of the floor.
$8m70cm=870cm$ and $6m38cm=638cm$
Finding HCF of $870;638$, we have
Prime Factorisation of $870=2\times 3\times 5\times 29$
$638=2\times 11\times 29$
We then choose each common prime number with the least power and multiply them to get the HCF.
$=>HCF=2\times 29=58$
So the dimensions of each square till be $58cm$
Now, least number of square tiles required $=\frac{Areaofthefloor}{Areaofeachtile}=\frac{870\times 638}{58\times 58}=165$