Question

Use Euclid's division algorithm to find the HCF of $900$ and $270$.

Answer 1

Finding the H.C.F:

According to Euclid’s Division Lemma if we have two positive integers $a$ and $b$, then there exist unique integers $q$ and$r$ which satisfies the condition

$a=bq+rwhere0\le r<b$

Consider two numbers $900$ and $270$, and we need to find the HCF of these numbers.

$\mathrm{Dividend}=\mathrm{Quotient}\times \mathrm{Divisor}+\mathrm{Remainder}$

When the reminder is zero then the quotient is the HCF.

$$\begin{gathered} 900=270\times 3+90 \\ 270=90\times 3+0 \end{gathered}$$

The remainder has now become zero.

Since the divisor at this stage is $90$.

Therefore, HCF$(900,270)=90$