If d is HCF of 56 and 72, then find x,y satisfying the equation d=56x+72y. Also show that x and y are not unique.

According to Euclid division Lemma,

72=56*1+1656

=16*3+816

=8*2+0…….

So, 8 is the HCF.

Now 8=56-(16*3)…..

8 is expressed in terms of 56 and 16, but it should be in the form of 56 and 72.

Hence by splliting 16 we get,

8=56-(72-56*1)(3)

8 =56-72*3+56*3…….

Since we have one more 56 is grouped as

8 =56*4+72(-3).

So,X and Y are 4,3 respectively ..

Therefore X and Y are not equal.

BOOK

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