Question

The greatest integer which can divide 0.18 and 2.7 so that both the quotients are integers is ___ .(Give answer till two decimal places)

Answer 1

Highest common factor (HCF) of two or more numbers is the greatest number which divides each of them exactly.

To get the greatest integer which can divide 0.18 and 2.7 so that both the quotients are integers, we should find the HCF of 0.18 and 2.7.

To find the HCF, we can convert the given decimals to integers by multiplying both of them by 100.
$0.18\times 100=18$
$2.7\times 100=270$
The product of prime factors of $18=2\times 3^2$
The product of prime factors of $270=2\times 3^3\times 5$

$\Rightarrow$ HCF of 18 and 270 = $2\times 3^2$ = 18
$\therefore$ The HCF of 0.18 and 2.7 = $\frac{18}{100}=0.18$