Question

Use Euclid’s division algorithm to find the HCF of :

(i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255

ans​

Answer 1

Answer:

answer of this question

Answer 2

Step-by-step explanation:

(i) HCF of 135 and 225:

Applying the Euclid’s lemma to 225 and 135, (where 225 > 135), we get

225 = (135 × 1) + 90

Since, 90 ≠ 0, therefore, applying the Euclid’s lemma to 135 and 90, we have:

135 = (90 × 1) + 45

But 45 ≠ 0

∴ Applying Euclid’s Lemma to 90 and 45, we get

90 = (45 × 2) + 0

Here, r = 0, so our process stops. Since, the divisor at the last step is 45,

∴ HCF of 225 and 135 is 45.

(ii) HCF of 196 and 38220:

We start dividing the larger number 38220 by 196, we get

38220 = (196 × 195) + 0

∵ r = 0

∴ HCF of 38220 and 196 is 196.

(iii) HCF of 867 and 255:

Here, 867 > 255

∴ Applying Euclid’s Lemma to 867 and 255, we get

867 = (255 × 3) + 102

Since, 102 ≠ 0, therefore, applying the Euclid’s lemma to 255 and 102, we have:

255 = (102 × 2) + 51

But 51 ≠ 0

∴ Applying Euclid’s Lemma to 102 and 51, we get

102 = (51 × 2) + 0

Here, r = 0, so our process stops. Since, the divisor at the last step is 51,

∴ HCF of 867 and 255 is 51.