102172262400 has 918 divisors, whose sum is σ = 405986917518. Its totient is φ = 24536678400.

The previous prime is 102172262393. The next prime is 102172262407. The reversal of 102172262400 is 4262271201.

102172262400 is a `hidden beast` number, since 1 + 0 + 2 + 17 + 22 + 624 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (102172262393) and next prime (102172262407).

It can be written as a sum of positive squares in 9 ways, for example, as 89252757504 + 12919504896 = 298752^2 + 113664^2 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (102172262407) by changing a digit.

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 53 ways as a sum of consecutive naturals, for example, 2492006380 + ... + 2492006420.

Almost surely, 2^102172262400 is an apocalyptic number.

102172262400 is a gapful number since it is divisible by the number (10) 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 102172262400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (202993458759).

102172262400 is an abundant number, since it is smaller than the sum of its proper divisors (303814655118).

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

102172262400 is an equidigital number, since it uses as much as digits as its factorization.

102172262400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 115 (or 64 counting only the distinct ones).

The product of its (nonzero) digits is 2688, while the sum is 27.

The spelling of 102172262400 in words is "one hundred two billion, one hundred seventy-two million, two hundred sixty-two thousand, four hundred".