81964800 has 162 divisors, whose sum is σ = 293248592. Its totient is φ = 21841920.

The previous prime is 81964777. The next prime is 81964807. The reversal of 81964800 is 846918.

It is a happy number.

81964800 is a `hidden beast` number, since 8 + 1 + 9 + 648 + 0 + 0 = 666.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (81964807) 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 17 ways as a sum of consecutive naturals, for example, 56889 + ... + 58311.

Almost surely, 2^81964800 is an apocalyptic number.

81964800 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 81964800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (146624296).

81964800 is an abundant number, since it is smaller than the sum of its proper divisors (211283792).

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

81964800 is a wasteful number, since it uses less digits than its factorization.

81964800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1455 (or 1433 counting only the distinct ones).

The product of its (nonzero) digits is 13824, while the sum is 36.

The square root of 81964800 is about 9053.4413346528. The cubic root of 81964800 is about 434.3859747413.

It can be divided in two parts, 8196 and 4800, that added together give a square (12996 = 114²).

The spelling of 81964800 in words is "eighty-one million, nine hundred sixty-four thousand, eight hundred".