Question

Find the HCF of 96 and 60 and express it in the form of 96x +60y . Where x and y are integers using EDL ( euclids divison lemma)

Answer 1

according to Euclid division lemma, any number a can be written as $\boxed{\bf{a=bq+r}}$ where, 0 ≤ r < b

HCF of 96 and 60 by using EDL :

so, we can write 96 in the form 60 by using Euclid division lemma

e.g., 96 = 60 × 1 + 36

again, we can write 60 in the form of 36 by using EDL,

e.g., 60 = 36 × 1 + 24

again, we can write 36 in the form of 24 by using EDL,

e.g., 36 = 24 × 1 + 12

again, we can write 24 in the form of 12 by using EDL,

e.g., 24 = 12 × 2 + 0

here, remainder, r = 0 so, HCF of 96 and 60 = 12

now, we have to write HCF of 96 and 60 in the form of 96x + 60y .

12 = 96x + 60y

or, 1 = 8x + 5y

if we choose x = 2 and y = -3

then, 8 × 2 + 5 × -3 = 1

Hence, HCF of 96 and 60 = 96(2) + 60(-3)

is in the form of 96x + 60y where x and y are integers.