What is the smallest natural number n such that n! is divisible by 990

Show that 27! Is divisible by 2^12 . What is the largest natural number n such that 27 ! Is divisible by 2^n ?

Show that 27! Is divisible by 2^12 . What is the largest natural number n such that 27 ! Is divisible by 2^n ?

if n is the smallest natural number such that n+2n+3n+* * * * * * *+99n is a perfect squre , then the number of digits in n^(2) is -

If N=2^(3)xx3^(7) , then What is the smallest number that you need to divisible by N in order to make it a perfect square ?

If n is the smallest natural number such that n+2n+3n+...+99n is a perfect square, then the number of digits in n^(2) is

In n is an even number, then the largest natural number by which n(n+1)(n+2) is divisible is

Let sigma(n) denotes the sum of digits of a natural number n .If N is the smallest natural number such that sigma(N)=2020 , then find the value of sigma(5N+2021)