Divisibility rules

A number is divisible by $4$ if its:

From $3$ to $41$ how many such numbers which are divisible by 3 and the sum of their digits is $9$, are ?

If the number $42573*$ is exactly divisible by $72$, then the minimum value of $*$ is:

The number $111111111111$ is divisible by

The greatest five digit number exactly divisible by $9$ and $13$ is

Which of the following number is divisible by $3$?

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?

The number $708\mathrm{M}29\mathrm{NO}$ is divisible by $99$. $\mathrm{M}, \mathrm{N}$ and $\mathrm{O}$ are all single digit numbers greater than $0$ and $(\mathrm{M} + \mathrm{N} + \mathrm{O})$ is less than $18$. What would be the value of $\mathrm{N}$?

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?

Sheldon Cooper has a five digit number which is represented as $103\mathrm{mn}$. When he divides it by $5$ and $11$, he gets $1$ as a remainder in each case. What is the value of $(\mathrm{m} \times \mathrm{n})?$

One fine day, Ghasiteram, a renowned sweet shop in Udaipur prepared $\left({\mathrm{k}}^2+\mathrm{k}+1\right)$ as total number of sweets. How many values of ' $\mathrm{k}$ ' are possible, for which the total number of sweets should be divisible by $15?$

If a six digit number $3\mathrm{a}7\mathrm{b}8\mathrm{c}$ is divisible by $33$, then find the value of $(\mathrm{a} + \mathrm{b} + \mathrm{c})$.

How many natural number up to$2001$ divisible by $3 \mathrm{or} 4$ but NOT by$5$?

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

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

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

Which of the following options is divisible by $3$?

The number $45789$is divisible by which of the single digit numbers _____.

If the seven-digit number$74x29y6$ is divisible by $72$ , then what will be the value of $\left(2x+3y\right)$?

If $7129p465$ is divisible by $9$, then the value of $p$ is: