Euclid’s Division Lemma/Algorithm Type Question

 Euclid’s Division Algorithm > Question 

EUCLID’S DIVISION ALGORITHM QUESTION

Q. If the HCF of 468 and 222 is expressed as 468x + 222y, then x = ? 

Solution : 

Here, 468 > 222, 

So, By Euclid’s division lemma,

468 = 222 × 2 + 24                        (i)

Here, Remainder is 24 ≠ 0, So, We apply euclid’s division lemma to 222 and 24.

222 = 24 × 9 + 6                          (ii)

Again,R is 6 ≠ 0, So, We apply euclid’s division lemma to 24 and 6.

24 = 6 × 4 + 0                              (iii)

At this stage remainder is 0, so the 

HCF(468, 222) = 6 

Now, from (ii) , 

6 = 222 – 24 × 9

6 = 222 – (468 – 222 × 2) × 9    

6 = 222 – 468 × 9 + 222 × 2 × 9

6 = 468 × (–9) + 222 × 19

So, Now we can write the HCF(468,222) can be written as 468 × (–9) + 222 × 19

So, it can be 

           468 × (x) + 222 × y

    →   468x + 222y

Here, we’ve expressed the HCF(468,222) in the form of 468x + 222y , 

Where x  =  –9 .

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