81972800 has 168 divisors, whose sum is σ = 248692416. Its totient is φ = 25896960.

The previous prime is 81972757. The next prime is 81972809. The reversal of 81972800 is 827918.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (35).

It is not an unprimeable number, because it can be changed into a prime (81972809) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 145319 + ... + 145881.

It is an arithmetic number, because the mean of its divisors is an integer number (1480312).

Almost surely, 2^81972800 is an apocalyptic number.

81972800 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 81972800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (124346208).

81972800 is an abundant number, since it is smaller than the sum of its proper divisors (166719616).

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

81972800 is a wasteful number, since it uses less digits than its factorization.

81972800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 605 (or 590 counting only the distinct ones).

The product of its (nonzero) digits is 8064, while the sum is 35.

The square root of 81972800 is about 9053.8831448169. The cubic root of 81972800 is about 434.4001067213.

The spelling of 81972800 in words is "eighty-one million, nine hundred seventy-two thousand, eight hundred".