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)
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according to Euclid division lemma, any number a can be written as 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.
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.
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