NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.1

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 


Exercise 1.1

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) Given numbers are 135 and 225

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

∴ The HCF of 135 and 225 is 45.

(ii) Given numbers are 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

196 = 196 x 1 + 0

∴ The HCF of 196 and 38220 is 196.

(iii) Given numbers are 255 and 867

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

∴ The HCF of 255 and 867 is 51.

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