Question

findHCF of 72 and96 by Euclid division lemma and express it in the form 96m +72n​

Answer 1

$\underline{\large{\mathbf{Answer \:\: :HCF(72,96)\:=\: 24}}}$

$\underline{\textbf{ Step by Step Solution }}$

Here we need to find the HCF of 2 Number ie: 72 & 96 by Euclid's Division algorithm .

So , here 72 < 96 therefore by using Euclid's Division algorithm ( a = b × q + r )

We have $\implies$

96 = 72 × 1 + 24 --- eq (1 )

( Dividend = 96 , Quotient = 1 , Divisor = 72 & Remainder = 24 )

-- Now taking the obtained divisor as dividend and remainder as divisor we have ---

$\implies$ 72 = 24 × 3 + 0

Therefore

$\boxed{\mathbf{HCF( \:72,96\: )\: = \:24 }}$

Now ATQ we need to convert 24 into 96m - 72n form

So from Equation 1 we have

24 = 96 -72 × 1

$\boxed{\mathbf{24 \:=\: 96\: (1)\: +\:72\: (-1) }}$

thus it's the required form 24 = 96m + 72n where m = 1 & n = -1

$\underline{\textbf{More Info ..}}$

Euclid's Division lemma

Given two positive integer a & b there exits unique integer q and r which satisfies

a = bq + r

where r ≥ 0 but less than b .