Question

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

Answer 1

Answer:

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

Step-by-step 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 $\neq 0$

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

$39=13\times 3+0$

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

$73=21\times 3+10$

Here, remainder = 10 $\neq 0$

On applying division algorithm on 21 and 10, we get

$21=10\times 2+1$

Here, remainder = 1 $\neq 0$

On applying division algorithm on 10 and 1, we get

$10=1\times 10+0$

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