381916800 has 288 divisors, whose sum is σ = 1387327500. Its totient is φ = 100024320.

The previous prime is 381916789. The next prime is 381916819. The reversal of 381916800 is 8619183.

It can be written as a sum of positive squares in 6 ways, for example, as 25160256 + 356756544 = 5016^2 + 18888^2 .

It is a tau number, because it is divible by the number of its divisors (288).

It is a super-3 number, since 3×381916800³ (a number of 27 digits) contains 333 as substring.

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 35 ways as a sum of consecutive naturals, for example, 2563126 + ... + 2563274.

Almost surely, 2^381916800 is an apocalyptic number.

381916800 is a gapful number since it is divisible by the number (30) 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 381916800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (693663750).

381916800 is an abundant number, since it is smaller than the sum of its proper divisors (1005410700).

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

381916800 is a wasteful number, since it uses less digits than its factorization.

381916800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 268 (or 248 counting only the distinct ones).

The product of its (nonzero) digits is 10368, while the sum is 36.

The square root of 381916800 is about 19542.6917286233. The cubic root of 381916800 is about 725.5314692036.

The spelling of 381916800 in words is "three hundred eighty-one million, nine hundred sixteen thousand, eight hundred".