Question

the greatest common devisor of two numbers is 23 and their sum is 184 .then the difference among the following is ?

Answer 1

$\textit{Number Theory}$
$\textit{If greatest common divisor of two number is 23, and their sum is 184,}$
$\textit{Find difference of both number.}$

$gcd(a,b) = 23$
$a + b = 184$
$\textit{For any real number k,}$
$a = 23k_1$
$b = 23k_2$
$23k_1+23k_2 = 184$
$23(k_1+k_2) = 184$
$k_1+k_2 = 8$
$k_2 = 8 - k_1$

$a= 23k_1$
$b = 184-23k_1$
$a - b = 23k_1 - 184 + 23k_1$
$a - b = 46k_1 - 184$
$\therefore a - b = 46(k_1 - 4)$