81464576400 has 405 divisors, whose sum is σ = 291086162913. Its totient is φ = 21098246400.

The previous prime is 81464576381. The next prime is 81464576429. The reversal of 81464576400 is 467546418.

The square root of 81464576400 is 285420.

It is a perfect power (a square), and thus also a powerful number.

81464576400 is a `hidden beast` number, since 8 + 14 + 64 + 576 + 4 + 0 + 0 = 666.

It can be written as a sum of positive squares in only one way, i.e., 29327247504 + 52137328896 = 171252^2 + 228336^2 .

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 1147388365 + ... + 1147388435.

Almost surely, 2^81464576400 is an apocalyptic number.

81464576400 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

81464576400 is the 285420-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 81464576400

81464576400 is an abundant number, since it is smaller than the sum of its proper divisors (209621586513).

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

81464576400 is a wasteful number, since it uses less digits than its factorization.

81464576400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 300 (or 148 counting only the distinct ones).

The product of its (nonzero) digits is 645120, while the sum is 45.

The spelling of 81464576400 in words is "eighty-one billion, four hundred sixty-four million, five hundred seventy-six thousand, four hundred".