what is actually Euclid's Division Lemma & Algorithm?please explaine in detail.
Lemma is nothing but the division fact.Its written like a = d.q + r
It means when a number (a) is divided by divisor(d), you get quotient(q) and remainder(r).
The above lemma can be used in algorithm for finding HCF.
For given two numbers,we divide the larger by the smaller.Obviously, the remainder thus obtained will be lesser than the divisor.We put this in division fact or lemma form.
Now , we take the divisor and remainder from above division. Divide the previous divisor by that remainder and
put it in lemma form.
Continue writing the lemma with succesive divisor and remainders till you get zero as remainder. At this stage
the last divisor will be required HCF.
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