77821200 has 90 divisors (see below), whose sum is σ = 270073674. Its totient is φ = 20751360.

The previous prime is 77821199. The next prime is 77821217. The reversal of 77821200 is 212877.

It can be written as a sum of positive squares in 3 ways, for example, as 451584 + 77369616 = 672^2 + 8796^2 .

It is a tau number, because it is divible by the number of its divisors (90).

It is a super-2 number, since 2×77821200² = 12112278338880000, which contains 22 as substring.

It is a hoax number, since the sum of its digits (27) coincides with the sum of the digits of its distinct prime factors.

It is an unprimeable number.

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, 7209 + ... + 14408.

Almost surely, 2^77821200 is an apocalyptic number.

It is an amenable number.

77821200 is an abundant number, since it is smaller than the sum of its proper divisors (192252474).

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

77821200 is a wasteful number, since it uses less digits than its factorization.

77821200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 21641 (or 21627 counting only the distinct ones).

The product of its (nonzero) digits is 1568, while the sum is 27.

The square root of 77821200 is about 8821.6325019806. The cubic root of 77821200 is about 426.9391434459.

The spelling of 77821200 in words is "seventy-seven million, eight hundred twenty-one thousand, two hundred".