What is the remainder when $2468$ is divided by $37$?

The sum of squares of two numbers is $80$ and the square of their difference is $36$. The product of the two numbers is

When a certain number is multiplied by $7$,the product consists entirely of fives; find the least value of such a number.

$A$ number is of two digits. The position of digits is interchanged and the new number is added to the original number. The resultant number will always be divisible by

$8000 \div 16 - 200 = ? \times 6$

When a number is divided by $56,$ the remainder is $29.$ If the same number is divided by $8,$ then the remainder will be: