82972800 has 288 divisors, whose sum is σ = 307472880. Its totient is φ = 21288960.

The previous prime is 82972751. The next prime is 82972847. The reversal of 82972800 is 827928.

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

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, 1238367 + ... + 1238433.

Almost surely, 2^82972800 is an apocalyptic number.

82972800 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 82972800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (153736440).

82972800 is an abundant number, since it is smaller than the sum of its proper divisors (224500080).

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

82972800 is a wasteful number, since it uses less digits than its factorization.

82972800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 140 (or 120 counting only the distinct ones).

The product of its (nonzero) digits is 16128, while the sum is 36.

The square root of 82972800 is about 9108.9406628872. The cubic root of 82972800 is about 436.1594120108.

Adding to 82972800 its product of nonzero digits (16128), we get a palindrome (82988928).

The spelling of 82972800 in words is "eighty-two million, nine hundred seventy-two thousand, eight hundred".