Question

1. Using the Euclidian algorithm, compute (91,39) and (73,21)

Answer 1

HCF(91,39) = 13 and HCF(73,21) = 1

Explanation:

As per euclidian algorithm, a = bq + r, where a is dividend, b is divisor, q is quotient and r is remainder.

We can use euclidian algorithm to find the HCF of numbers.

To find: HCF ( 91, 39 ):

On dividing 91 by 39, we get

91=39×2+13

Here, remainder = 13
`\\eq 0`

So, again applying division algorithm on 39 and 13, we get

`39=13* 3+0`

As remainder = 0 and divisor at this step is equal to 13, HCF = 13 .

To find: HCF ( 73, 21 )

On dividing 73 by 21, we get

`73=21* 3+10`

Here, remainder = 10
`\\eq 0`

On applying division algorithm on 21 and 10, we get

`21=10* 2+1`

Here, remainder = 1
`\\eq 0`

On applying division algorithm on 10 and 1, we get

`10=1* 10+0`

As remainder = 0 and divisor at this step is 1, HCF = 1