Question

the greater no. that will divide 76,112,172 and 184 so as to leave reminder 40in each case is k square-3 . find the value of k​

Answer 1

Answer:

The value of

$\bf{k=\pm\sqrt{15}}}$

Step-by-step explanation:

Given:

$\text{76, 112, 172, 184 leave reminder 40 when divided by k^2-3 }$

$\implies\:\text{The G.C.D of 36, 72, 132, 144 is k^2-3 }$

$36=2^2\times3^2$

$72=2^3\times3^2$

$132=2^2\times3\times11$

$144=2^4\times3^2$

$\text{Now, by factorization, The G.C.D of 36,72,132,144 is 12}$

$\implies\:k^2-3=12$

$\implies\:k^2=15$

$\implies\:\boxed{\bf{k=\pm\sqrt{15}}}$