21101414400 has 864 divisors, whose sum is σ = 86501338560. Its totient is φ = 4866048000.

The previous prime is 21101414387. The next prime is 21101414417. The reversal of 21101414400 is 441410112.

21101414400 is a `hidden beast` number, since 211 + 0 + 1 + 414 + 40 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 116582310 + ... + 116582490.

It is an arithmetic number, because the mean of its divisors is an integer number (100117290).

Almost surely, 2^21101414400 is an apocalyptic number.

21101414400 is a gapful number since it is divisible by the number (20) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 21101414400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (43250669280).

21101414400 is an abundant number, since it is smaller than the sum of its proper divisors (65399924160).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

21101414400 is a wasteful number, since it uses less digits than its factorization.

21101414400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 253 (or 225 counting only the distinct ones).

The product of its (nonzero) digits is 128, while the sum is 18.

Adding to 21101414400 its reverse (441410112), we get a palindrome (21542824512).

The spelling of 21101414400 in words is "twenty-one billion, one hundred one million, four hundred fourteen thousand, four hundred".