Question

According to Euclid's division algorithm, using Euclid's division lemma for any two positive integers $a$ and $b$ with $a>b$ enables us to find the

• A. HCF
• B. LCM
• C. Decimal expansion
• D. Quotient

Answer 1

The correct option is A HCF

According to Euclid's division lemma,

For each pair of positive integers $a$ and $b$, we can find unique integers $q$ and $r$ satisfying the relation
$a=bq+r,0\le r<b$

If $r=0$ then q will be HCF of $a$ and $b$

The basis of the Euclidean division algorithm is Euclid’s division lemma.

To calculate the Highest Common Factor (HCF) of two positive integers $a$ and $b$ we use Euclid’s division algorithm.

HCF is the largest number which exactly divides two or more positive integers.

By exactly we mean that on dividing both the integers $a$ and $b$ by HCF, the remainder is zero.

So correct answer is option A