Question

hcf of 70 and 30 is expressible in the form of 70=30×+10 then the value of x is​

Answer 1

$\bf \blue{Given \:that :}$

70 and 30

$\bf \pink{To \:Find:}$

HCF and LCM of these two numbers as a linear combination of ax + by , the find the the values of x and y?

$\bf \green{Solution:}$

By Euclid's Division Lemma , HCF of 70 and 30 can be found in the following way:-

$\sf \purple{70 = 30  \times  2 + 10    - (1)} \\ </h3><h3> \sf \orange{And, 30 = 10  \times  3 + 0}$

The least non zero remainder obtained is 10 

So,

$\sf HCF \: of \: \green{ 70 \: and \: 30} \: is \purple{= 10}$

$\sf <strong>Now,</strong> \blue{let  10 = 70x  + 30y} \\ </h3><h3> \sf From \: \red{eq (1)} we \: see \: that : \\ </h3><h3> \sf \pink{10 = 70 - (30 \times  2)}$

$\sf On \: comparing \: we \: get \: that \: \orange{x = 1 \: and \: y = -2 }$

$\sf Hence, \: value \: of \: \red{ x} \: is \: \pink{ 1 \: and \: y} \: is \: \green{(-2)}  </h3><p>$