382972800 has 384 divisors, whose sum is σ = 1487404800. Its totient is φ = 84787200.

The previous prime is 382972783. The next prime is 382972817. The reversal of 382972800 is 8279283.

It is an interprime number because it is at equal distance from previous prime (382972783) and next prime (382972817).

It is a tau number, because it is divible by the number of its divisors (384).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 2755131 + ... + 2755269.

It is an arithmetic number, because the mean of its divisors is an integer number (3873450).

Almost surely, 2^382972800 is an apocalyptic number.

382972800 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 382972800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (743702400).

382972800 is an abundant number, since it is smaller than the sum of its proper divisors (1104432000).

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

382972800 is a wasteful number, since it uses less digits than its factorization.

382972800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 214 (or 197 counting only the distinct ones).

The product of its (nonzero) digits is 48384, while the sum is 39.

The square root of 382972800 is about 19569.6908509051. The cubic root of 382972800 is about 726.1995520329.

The spelling of 382972800 in words is "three hundred eighty-two million, nine hundred seventy-two thousand, eight hundred".