Question

Use euclid's division algorithm to find the gcf of 441,567 and 693

Answer 1

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Q. is Find the H.C.F of 441, 567 and 693

sol.
By Euclid's division lemma on 441 and 567 .

since, 567 > 441
for every point of integers A and B there exist unique integer q and r
such that a = bq + r
where 0 ≤ r < b

so here and a > b
a = 567 and b = 441 ,so

=> 567 = 441 × 1 + 126
=> 441 = 126 × 3 + 63
=> 126 = 63 × 2 + 0

Here r = 0 , so H.C.F of 567 and 441 is 63 .

now , apply Euclid's division lemma on 63 and 693
here , a = 693 and b = 63 , so that a > b

=> 693 = 63 × 11 + 0
here, r = 0 , so H.C.F of 63 and 693 is 11


::::: H.C.F of 441, 567 and 683 is 11.
Answer is 11

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