This page offers a step-by-step solution to the specific question **NCERT Class 10th Mathematics - Real Numbers | use euclid rsquo s division algorithm to find the Answer ** from NCERT Class 10th Mathematics, Chapter Real Numbers.

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, we have to find H.C.F of 135 and 225

First divide divide the larger integer smaller integer

Since, 225 > 135

Therefore, by Euclid’s Division algorithm

225 = 135 × 1 + 90 (i)

Here 90 ≠ 0, so proceed the same procedure further

Again by E.D.L, (E.D.L = Euclid’s division algorithm)

135 = 90 × 1 + 45 (ii)

As we know, 45 ≠ 0 therefore, again by E.D.L

90 = 45 × 2 + 0 (iii)

Here, r = 0 so we cannot proceed further. The divisor at this Stage is 45.

From (i), (ii) and (iii)

H.C.F (225, 135) = H.C.F (135, 90) = H.C.F (90, 45) = 45.

**(ii)** Here, we have to find H.C.F of 38220 and 196

First divide the larger integer smaller integer

Since, 3822 > 196

Therefore by Euclid’s Division Algorithm

38220 = 196 × 195 + 0

Here, r = 0 so we cannot proceed further. The divisor at this Stage is 196.

Hence, H.C.F (38220, 196) = 196.

**(iii)** Here, we have to find H.C.F of 867 and 255

First divide the larger integer smaller integer

Since, 867 > 255

Therefore, by Euclid’s Division algorithm

867 = 255 × 3 + 102 (i)

Remainder 102 ≠ 0, so proceed the same procedure further using E.D.L

255 = 102 × 2 + 51 (ii)

Here, 51 ≠ 0 again using E.D.L = 51 × 2

102 = 51 × 2 + 0 (iii)

Here, r = 0 so we cannot proceed further. The divisor at this Stage is 51.

From (i), (ii) and (iii)

H.C.F (867, 255) = H.C.F (255, 102) = H.C.F (102, 51) = 51.

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