829957440400 has 405 divisors, whose sum is σ = 2268945195097. Its totient is φ = 291526400000.

The previous prime is 829957440397. The next prime is 829957440409. The reversal of 829957440400 is 4044759928.

The square root of 829957440400 is 911020.

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

It can be written as a sum of positive squares in 13 ways, for example, as 513555690384 + 316401750016 = 716628^2 + 562496^2 .

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (829957440409) by changing a digit.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 8217400350 + ... + 8217400450.

Almost surely, 2^829957440400 is an apocalyptic number.

829957440400 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

829957440400 is the 911020-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 829957440400

829957440400 is an abundant number, since it is smaller than the sum of its proper divisors (1438987754697).

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

829957440400 is a wasteful number, since it uses less digits than its factorization.

829957440400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 324 (or 160 counting only the distinct ones).

The product of its (nonzero) digits is 2903040, while the sum is 52.

The spelling of 829957440400 in words is "eight hundred twenty-nine billion, nine hundred fifty-seven million, four hundred forty thousand, four hundred".