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Q.

Calculate the HCF of 441, 567, and 693 using Euclid's division algorithm.


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a

36

b

40

c

63

d

25 

answer is C.

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Detailed Solution

Given numbers are,
441, 567, and 693
According to Euclid’s division lemma, if we have two positive integers say m and n, then there exist unique integers q and r which satisfies
m=nq+r,  where 0≤r<n.
First we take m=693 and n=567 then,
⇒693=567×1+126 ⇒567=126×4+63 ⇒126=63×2+0  
∴ HCF 693,567 =63.  
Now, we find HCF of 441 and 63.
Consider, m=441 and n=63 then,
⇒441=63×7+0  
Therefore, HCF 693,567,441 =63.  
Hence, the correct option is 3.
 
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