Question

Use euclid's division lemma to find the hcf of 8262 and 101592

Answer 1

Hi ,

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Euclid's division lemma :

Let a and b be any two positive Integers .

Then there exist two unique whole numbers

q and r such that

a = bq + r ,

0 ≤ r < b

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Now ,

start with a larger interger , that is 101592 ,

Apply the division lemma to 101592 and

8262 ,

101592 = 8262 × 12 + 2448

8262 = 2448 × 3 + 918

2448 = 918 × 2 + 612

918 = 612 × 1 + 306

612 = 306 × 2 + 0

The remainder has now become zero , so

our procedure stops.

Since the divisor at this stage is 306 .

Therefore ,

HCF ( 101592 , 8262 ) = 306

I hope this helps you.

: )

Answer 2

Answer to the question :

We know that Euclid's division Lemma is x and y for any two positive integers, there exist unique integers q and r satisfactorily x = yq + r, where 0 ≤ r <y. In case r=0 then y will be the HCF. Here we see 101592> 8262

Now,
101592= 8262×12+2448
8262=2448×3+918
2448=918×2+612
918=612×1+306
612=306×2+0

Hence, finally we have found the remainder (r)= 0
So, HCF (101592,8262)= 306
The answer is 306