8221188268800 has 432 divisors, whose sum is σ = 32465211989280. Its totient is φ = 2023676559360.

The previous prime is 8221188268723. The next prime is 8221188268801. The reversal of 8221188268800 is 88628811228.

8221188268800 is a `hidden beast` number, since 8 + 221 + 1 + 88 + 268 + 80 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (432).

It is a Harshad number since it is a multiple of its sum of digits (54).

It is not an unprimeable number, because it can be changed into a prime (8221188268801) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 416542 + ... + 4076258.

Almost surely, 2^{8221188268800} is an apocalyptic number.

8221188268800 is a gapful number since it is divisible by the number (80) 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 8221188268800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (16232605994640).

8221188268800 is an abundant number, since it is smaller than the sum of its proper divisors (24244023720480).

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

8221188268800 is a wasteful number, since it uses less digits than its factorization.

8221188268800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3659765 (or 3659740 counting only the distinct ones).

The product of its (nonzero) digits is 1572864, while the sum is 54.

The spelling of 8221188268800 in words is "eight trillion, two hundred twenty-one billion, one hundred eighty-eight million, two hundred sixty-eight thousand, eight hundred".