Use Euclid’s Division Algorithm to Find Hcf of Numbers Maths Exercise 1.1 Chapter 1 Real Numbers Maths Class 10

Question 1. Use Euclid’s division algorithm to find the HCF of :
(i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255

Answer: (i)

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)

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)
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