Question

The HCF of 114 and 76 is of the form 114-76p. Find the value of p​

Answer 1

HCF of 114 and 76 is 38
114 - 76p = 38
76p = 114-38
76p = 76
p = 76/76 = 1

Answer 2

$\large \bold{ \underline{ \underline{ \sf \: Answer : \: \: \: }}}$

$\to$ p = 1

$\large \bold{ \underline{ \underline{ \sf \: Explaination : \: \: \: }}}$

$\huge \star$ Prime factorisation of 114 :

114 = 2 x 3 x 19

$\huge \star$ Prime factorisation of 76 :

76 = 2 x 2 x 19

Therefore ,

HCF ( 114 , 76 ) = 2 × 19 = 38

According to the question ,

$\to \sf 38 = 114 - 76p \\ \\\to \sf </p><p>38 - 114 = - 76p \\ \\ \to \sf </p><p>- 76p = - 76 \\ \\ \to \sf </p><p>p = \frac{76}{76} \\ \\ \to \sf </p><p>p = 1$

Hence , the required value is 1