Question

Hcf of 99 and 81 by euclids algorithm ​

Answer 1

to find the hcf of any two or more numbers. here we've 2 numbers so follow the steps given below :-

⏹ first of all, you've to divide the greater number by smaller number. here 99 by 81.

⏺ then divide the smaller number by the remainder. like here the remainder comes 18. now divide 81 by 18.

⏹ now, dividend the previous remainder (18) and divisor the current remainder (9)

⏺ you've to continue doing this until you get 0 as remainder. and the last number by which you've divided and the remainder comes 0 is your answer. I mean Hcf.

here, we took 9 as the divisor when remainder comes 0.

so the Hcf of 81 and 99 is 9.

refer to the attachment if you wanna know how I solved it.

now according to Euclid's division algorithm, a = bq + r where 0 ≤ r ≤ b

• a = dividend
• b = divisor
• q = quotient
• r = remainder

➡ 99 = 81 × 1 + 18

➡ 81 = 18 × 4 + 9

➡ 18 = 9 × 2 + 0

b is the HCF after the remainder comes 0.

hence, it's proved that 9 is the HCF of 81 and 99.

Answer 2

Answer :-

HCF = 9

Given :-

Numbers 99 and 81 .

To find :-

It's HCF by Euclid division algorithm.

Solution:-

Euclid division algorithm :- Let a and b be any positive integer Where a > b when a is divided by b gives q as quoteint and r as remainder satisfying the equation.

→ a = bq + r

Now,

Let a = 99 and b = 81

Applying Euclid division algorithm,

→$a = bq + r$

→$99 = 81 \times 1 + 18$

→$81 = 18 \times 4 + 9$

→$18 = 9 \times 2 + 0$

$\boxed{\sf{ HCF = 9 }}$

At this step remainder is 0

Therefore,

HCF will be 9.