Q. 194.1( 25 Votes )

Use Euclid’s algo

Answer :

Given numbers are 4052 and 12576


Here, 12576 > 4052


So, we divide 12576 by 4052


By using Euclid’s division lemma, we get


12576 = 4052 × 3 + 420


Here, r = 420 ≠ 0.


On taking 4052 as dividend and 420 as the divisor and we apply the Euclid’s division lemma, we get


4052 = 420 × 9 + 272


Here, r = 272 ≠ 0


On taking 420 as dividend and 272 as the divisor and again we apply the Euclid’s division lemma, we get


420 = 272 × 1 + 148


Here, r = 148 ≠ 0


On taking 272 as dividend and 148 as the divisor and again we apply the Euclid’s division lemma, we get


272 = 148 × 1 + 124


Here, r = 124 ≠ 0.


On taking 148 as dividend and 124 as the divisor and we apply the Euclid’s division lemma, we get


148 = 124 × 1 + 24


Here, r = 24 ≠ 0


So, on taking 124 as dividend and 24 as the divisor and again we apply the Euclid’s division lemma, we get


124 = 24 × 5 + 4


Here, r = 4 ≠ 0


So, on taking 24 as dividend and 4 as the divisor and again we apply the Euclid’s division lemma, we get


24 = 4 × 6 + 0


The remainder has now become 0, so our procedure stops. Since, the divisor at this last stage is 4, the HCF of 4052 and 12576 is 4.


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