816379200 has 756 divisors, whose sum is σ = 3675819420. Its totient is φ = 170311680.

The previous prime is 816379189. The next prime is 816379259. The reversal of 816379200 is 2973618.

816379200 is a `hidden beast` number, since 81 + 6 + 379 + 200 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 189778176 + 626601024 = 13776^2 + 25032^2 .

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 107 ways as a sum of consecutive naturals, for example, 9172756 + ... + 9172844.

It is an arithmetic number, because the mean of its divisors is an integer number (4862195).

Almost surely, 2^816379200 is an apocalyptic number.

816379200 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 816379200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1837909710).

816379200 is an abundant number, since it is smaller than the sum of its proper divisors (2859440220).

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

816379200 is a wasteful number, since it uses less digits than its factorization.

816379200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 144 (or 119 counting only the distinct ones).

The product of its (nonzero) digits is 18144, while the sum is 36.

The square root of 816379200 is about 28572.3502708475. The cubic root of 816379200 is about 934.6104738310.

The spelling of 816379200 in words is "eight hundred sixteen million, three hundred seventy-nine thousand, two hundred".