Factors and Divisors

Find the number of positive integers that are divisors of at least one of the numbers ${\text{10}}^{10}{\text{; 18}}^{11}\text{;}{15}^7$.

Find the product of all the factors of the given number.

$16$

Find the product of all the factors of the given number.

$12$

In how many ways $3600$ can be resolved as a product of two different factors.

In how many ways $2500$ can be resolved as a product of two different factors.

In how many ways the number $10800$ can be resolved as a product of two different factors.

In how many ways $8100$ can be resolved as a product of two different factors.

In how many ways can $38808$ be expressed as a product of two co primes?

In how many ways can $1200$ be expressed as a product of two co primes?

If the integers from $1$ to $2021$ are written as a single integer like $123\dots 91011\dots 20202021$, then the ${2021}^{\mathrm{st}}$ digit (counted from the left) in the resulting number is

Let $N$ be the least positive integer such that whenever a non-zero digit $C$ is written after the last digit of $N$, the resulting number is divisible by $C$. The sum of the digits of $N$ is

For any natural number $n$, $\left(15\times 5^{2n}\right)+\left(2\times 2^{3n}\right)$ is divisible by

Let $f\left(n\right)=$ $\sum _{r=0}^n\sum _{k=r}^n{}^{k}C_r$, then total number of divisors of $f\left(11\right)$ is equal to :

The number of divisors of $7!$is

Total number of divisors of number $480$ that are of the form $4n+2,$ $n\in W=$

Consider the following statements:

$\left(i\right)$ The product of $r$ consecutive natural numbers is always divisible by $r!$.

$\left(ii\right)$ The total number of proper positive divisors of $115500$ is $94$.

$\left(iii\right)$ A pack of $52$ cards can be divided equally among four players in $\frac{52!}{{\left(\mathrm{13!}\right)}^4}$ ways.

Which of the statement given above is(are) correct ?

Total number of divisors of number $480$ that are of the form $4n+2, n\in W=$

Let $x_1,x_2,x_3,\dots ,x_k$ are the total divisors of positive integer n. If $\sum _{i=1}^k{x}_i=93$ and $\sum _{i=1}^k\frac{1}{x_i}=\frac{93}{50},$ then the value of k is

Number of divisors of $2^2,3^3,5^3,7^5$ of the form $4n + 1$ , $nϵN$ is

The number of ways to write 30 as the product of natural numbers m and n, such that g.c.d(, n) = 1 is