Divisibility

A number is divisible by $4$ if its:

When $n$ is divided by $4$, the remainder is $3$. What is the remainder when $2n$ is divided by $4$?

If all the numbers from $5$ to $80$, which are divisible by $5$ are written in descending order, then which of the numbers will occupy ${11}^{th}$ place from the top ?

The sum of two consecutive odd number is always divisible by:

The least perfect square number which is divisible by$3,4, 5, 6$ and $8$ is_____.

When the numbers $19779$ and $17997$ are divided by a certain three digit number, they leave the same remainder. How many such divisors are there?

If A is the smallest three-digit number divisible by both $6$ and $7$ and B is the largest four digit number divisible by both $6$ and $7$, then what is the value of B$-$A?

$m$ and $n$ are two positive integers satisfying $1<m<n\le 40.$ Find the number of pairs of $(m, n)$ such that their product $mn$ is divisible by $33.$

Find the smallest positive integer $n$ such that $n(n+1)$ $(n+2)$ is divisible by $247.$

$2ab5$ is a four digit number divisible by $25.$ If the number formed from the two digits $ab$ is a multiple of $13,$ then find $ab.$

Amy Farrah Fowler works in the computational molecular biology department, University of CalTech. Her boss Sheldon Cooper asked her to form five-digit numbers using digits $0, 2, 3, 4, 5, 6$ in such a way that no digit is used more than once. Sheldon has also asked Amy to ensure that the numbers are exactly divisible by $8$. Amy can form how many numbers?

If the number $62783xy$ is divisible by both $8$ and $5$, then the smallest possible value of $x$ and $y$ is:

What should be the value of $\mathrm{N}$ to make $396258\mathrm{N}$divisible by $8$?

Which of the following is exactly divisible by $6$?

If $r$ is the remainder when each of $4749, 5601$ and$7092$ is divided by the greatest possible number $d (>1)$, then the value of $(d + r)$ will be _____.

Which of the following numbers is divisible by both $7$ and $11$?

Which of the following numbers is divisible by $6$?

The largest number which should replace $x$ in the number $2365x4$ to make the number divisible by $4$ is: 

If the number $1005x4$ is completely divisible by $8$, then the smallest integer in place of $x$ will be:

A $5$-digit number $\overline{abcde}$, when multiplies by $9$, gives the $5$-digit number $\overline{edcba}$. The sum of the digits in the number is