CBSE Class 10 Maths Euclid's Division Lemma and Algorithm

Solution

In the given pair, 38220 > 196, thus let 38220 = a and 196 = b.

Now by applying the Euclid’s division algorithm a = bq + r, we get

38220 = 196 × 195 + 0

Since in the above equation we get r = 0; therefore, 196 is the HCF of the given pair 196 and 38220. 

Solution

In the given pair, 225 > 135, thus let 225 = a and 135 = b.

Now by applying the Euclid’s division algorithm a = bq + r, we get

225 = 135 × 1 + 90

135 = 90 × 1 + 45

90 = 45 × 2 + 0

Since in the above equation we get r = 0; therefore, 45 is the HCF of the given pair 225 and 135. 

Solution

Euclid’s division lemma states that for two positive integers a and b, there exists unique integers q and r such that a = bq + r, where r must satisfy 0 £ r < b.