Question

if h is equal to if H=HCF of a and b , then H=na +mb where m and n are integers. verify the above result for a=237 and b=81.​

Answer 1

Step-by-step explanation:

Using Euclid's division algorithm for 384 and 26, we have

here, 384>26;

∴, 384=26×14+20 --------------(1)

26=20×1+6 ----------------------(2)

20=6×3+2 -----------------------(3)

6=2×3+0

since the remainder is 0, then d=HCF(a,b)=HCF(384,26)=2

Now, from (3) we get,

2=20-(6×3)

or, 2=20-{26-(20×1)}×6 ; [using (2)]

or, 2=26×6+20×(1+1×6)

or, 2=26×6+20×7

or, 2=26×6+{384-(26×14)}×7 ; [using (1)]

or, 2=384×7+26×(6-14×7)

or, 2=384×7+26×(6-98)

or, 2=384×7+26×(-92)

∴, d=na+mb=7×384+(-92)×26

i.e., n=7, m=-92

Answer 2

Answer:

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