Using Euclid's division algorithm, find the HCF of
(i) 612 and 1314
(ii) 1260 and 7344
(iii) 4052 and 12576
(i) 612 and 1314
612 < 1314
Thus, we divide 1314 by 612 by using Euclid's division lemma
1314 = 612 × 2 + 90
∵ Remainder is not zero,
∴ we divide 612 by 90 by using Euclid's division lemma
612 = 90 × 6 + 72
∵ Remainder is not zero,
∴ we divide 90 by 72 by using Euclid's division lemma
90 = 72 × 1 + 18
∵ Remainder is not zero,
∴ we divide 72 by 18 by using Euclid's division lemma
72 = 18 × 4 + 0
Since, Remainder is zero,
Hence, HCF of 612 and 1314 is 18.
(ii) 1260 and 7344
1260 < 7344
Thus, we divide 7344 by 1260 by using Euclid's division lemma
7344 = 1260 × 5 + 1044
∵ Remainder is not zero,
∴ we divide 1260 by 1044 by using Euclid's division lemma
1260 = 1044 × 1 + 216
∵ Remainder is not zero,
∴ we divide 1044 by 216 by using Euclid's division lemma
1044 = 216 × 4 + 180
∵ Remainder is not zero,
∴ we divide 216 by 180 by using Euclid's division lemma
216 = 180 × 1 + 36
∵ Remainder is not zero,
∴ we divide 180 by 36 by using Euclid's division lemma
180 = 36 × 5 + 0
Since, Remainder is zero,
Hence, HCF of 1260 and 7344 is 36.
(iii) 4052 and 12576
4052 < 12576
Thus, we divide 12576 by 4052 by using Euclid's division lemma
12576 = 4052 × 3 + 420
∵ Remainder is not zero,
∴ we divide 4052 by 420 by using Euclid's division lemma
4052 = 420 × 9 + 272
∵ Remainder is not zero,
∴ we divide 420 by 272 by using Euclid's division lemma
420 = 272 × 1 + 148
∵ Remainder is not zero,
∴ we divide 272 by 148 by using Euclid's division lemma
272 = 148 × 1 + 124
∵ Remainder is not zero,
∴ we divide 148 by 124 by using Euclid's division lemma
148 = 124 × 1 + 24
∵ Remainder is not zero,
∴ we divide 124 by 24 by using Euclid's division lemma
124 = 24 × 5 + 4
∵ Remainder is not zero,
∴ we divide 24 by 4 by using Euclid's division lemma
24 = 4 × 6 + 0
Since, Remainder is zero,
Hence, HCF of 4052 and 12576 is 4.
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