872142616800 has 2160 divisors, whose sum is σ = 4074051244032. Its totient is φ = 177591398400.

The previous prime is 872142616789. The next prime is 872142616811. The reversal of 872142616800 is 8616241278.

872142616800 is a `hidden beast` number, since 8 + 7 + 21 + 4 + 2 + 616 + 8 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (872142616789) and next prime (872142616811).

It is a tau number, because it is divible by the number of its divisors (2160).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 359 ways as a sum of consecutive naturals, for example, 2376410217 + ... + 2376410583.

Almost surely, 2^872142616800 is an apocalyptic number.

872142616800 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 872142616800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2037025622016).

872142616800 is an abundant number, since it is smaller than the sum of its proper divisors (3201908627232).

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

872142616800 is a wasteful number, since it uses less digits than its factorization.

872142616800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 463 (or 428 counting only the distinct ones).

The product of its (nonzero) digits is 258048, while the sum is 45.

The spelling of 872142616800 in words is "eight hundred seventy-two billion, one hundred forty-two million, six hundred sixteen thousand, eight hundred".