Question

Find a number which when divided by $39$ gives a remainder $16$ and when divided by $56$ gives a remainder $27$. How many such numbers are there?

Answer 1

$⟹$$x=39p+16$
$x=56q+27$
$39p+16=56q+27$
$39p-56q=11$
No such numbers are possible for $p,q\in I$