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Use Euclid’s division algorithm to find the HCF of: (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255

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Answer :
(i) 135 and 225
Since 225 > 135, we apply the division lemma to 225 and 135 to obtain
225 = 135 × 1 + 90
Since remainder 90 ≠ 0, we apply the division lemma to 135 and 90 to obtain
135 = 90 × 1 + 45
We consider the new divisor 90 and new remainder 45, and apply the division lemma to obtain
90 = 2 × 45 + 0
Since the remainder is zero, the process stops.
Since the divisor at this stage is 45,
Therefore, the HCF of 135 and 225 is 45.
(ii) 196 and 38220
Since 38220 > 196, we apply the division lemma to 38220 and 196 to obtain
38220 = 196 × 195 + 0
Since the remainder is zero, the process stops.
Since the divisor at this stage is 196,
Therefore, HCF of 196 and 38220 is 196.
(iii) 867 and 255
Since 867 > 255, we apply the division lemma to 867 and 255 to obtain
867 = 255 × 3 + 102
Since remainder 102 ≠ 0, we apply the division lemma to 255 and 102 to obtain

255 = 102 × 2 + 51
We consider the new divisor 102 and new remainder 51, and apply the division lemma to obtain
102 = 51 × 2 + 0
Since the remainder is zero, the process stops.
Since the divisor at this stage is 51, Therefore, HCF of 867 and 255 is 51.

by (10 points)
in the solution
90=2 *45+0 is given the the hcf should be 2 right then how 45 is the hcf
by (128k points)
it is given that the hcf of 135 and 225 is 45 as the remainder is zero
by (10 points)
thank u i understood the sum
+1 vote
by (50.8k points)

(i) HCF of 135 and 225

Here 225 > 135 we always divide greater number with smaller one.
Divide 225 by 135 we get 1 quotient and 90 as remainder so that
225= 135*1 + 90
Divide 135 by 90 we get 1 quotient and 45 as remainder so that
135= 90*1 + 45
Divide 90 by 45 we get 2 quotient and no remainder so we can write it as
90 = 2*45+ 0
As there are no remainder so deviser 45 is our HCF

(ii) HCF of 196 and 38220 :

38220>196 we always divide greater number with smaller one.
Divide 38220 by 196 then we get quotient 195 and no remainder so we can write it as
38220 = 196 * 195 + 0
As there is no remainder so deviser 196 is our HCF

(iii) HCF of 867 and 255
867>255 we always divide greater number with smaller one.
divide 867 by 255 then we get quotient 3 and remainder is 102
so we can write it as
867 = 255 * 3 + 102
Divide 255 by 102 then we get quotient 2 and remainder is 51
So we can write it as
255 = 102 * 2 + 51
Divide 102 by 51 we get quotient 2 and no remainder
So we can write it as
102 = 51 * 2+ 0
As there is no remainder so deviser 51 is our answer

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