821552400 has 180 divisors, whose sum is σ = 3001318320. Its totient is φ = 207532800.

The previous prime is 821552377. The next prime is 821552401. The reversal of 821552400 is 4255128.

It is a happy number.

821552400 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (180).

It is not an unprimeable number, because it can be changed into a prime (821552401) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 62395 + ... + 74405.

Almost surely, 2^821552400 is an apocalyptic number.

821552400 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 821552400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1500659160).

821552400 is an abundant number, since it is smaller than the sum of its proper divisors (2179765920).

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

821552400 is a wasteful number, since it uses less digits than its factorization.

821552400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 12054 (or 12040 counting only the distinct ones).

The product of its (nonzero) digits is 3200, while the sum is 27.

The square root of 821552400 is about 28662.7353893518. The cubic root of 821552400 is about 936.5804530238.

The spelling of 821552400 in words is "eight hundred twenty-one million, five hundred fifty-two thousand, four hundred".