220824806400 has 891 divisors, whose sum is σ = 878944112683. Its totient is φ = 52931788800.

The previous prime is 220824806387. The next prime is 220824806467. The reversal of 220824806400 is 4608428022.

It is a happy number.

The square root of 220824806400 is 469920.

It is a perfect power (a square), and thus also a powerful number.

220824806400 is a `hidden beast` number, since 2 + 2 + 0 + 8 + 2 + 4 + 8 + 0 + 640 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 45953639424 + 174871166976 = 214368^2 + 418176^2 .

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 2481177556 + ... + 2481177644.

Almost surely, 2^220824806400 is an apocalyptic number.

220824806400 is a gapful number since it is divisible by the number (20) formed by its first and last digit.

220824806400 is the 469920-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 220824806400

220824806400 is an abundant number, since it is smaller than the sum of its proper divisors (658119306283).

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

220824806400 is a wasteful number, since it uses less digits than its factorization.

220824806400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 236 (or 110 counting only the distinct ones).

The product of its (nonzero) digits is 49152, while the sum is 36.

Multiplying 220824806400 by its sum of digits (36), we get a square (7949693030400 = 2819520²).

220824806400 divided by its sum of digits (36) gives a square (6134022400 = 78320²).

The spelling of 220824806400 in words is "two hundred twenty billion, eight hundred twenty-four million, eight hundred six thousand, four hundred".