Question

Find the HCF of $15$ and $18$ using Euclids Division Lemma.

• A. 6
• B. 2
• C. 3
• D. 1

Answer 1

Answer: (C)

Euclid’s division lemma

For any two positive integers $a$ and $b$, there exists unique integers $q$ and $r$ which satisfies the condition $a=bq+r$ where $0\le b<r$.

In $a=bq+r$,

if $r=0$ then $b$ is called HCF of $(a,b)$.

Given numbers are, $18$ and $15$.

Since, $18>15$.

Dividend $\left(a\right)=18$ and the divisor (b)=15$

Step 1:

$18=15\times 1+3$

Step 2:

$15=3\times 5+0$

Here the remainder is $0$.

$\Rightarrow$ HCF of $18$ and $15$ is $3$.

Hence, Option D is correct.