827044736400 has 405 divisors, whose sum is σ = 3004846005889. Its totient is φ = 210636222720.

The previous prime is 827044736389. The next prime is 827044736407. The reversal of 827044736400 is 4637440728.

The square root of 827044736400 is 909420.

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

827044736400 is a `hidden beast` number, since 82 + 70 + 447 + 3 + 64 + 0 + 0 = 666.

It can be written as a sum of positive squares in only one way, i.e., 297736105104 + 529308631296 = 545652^2 + 727536^2 .

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

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (827044736407) 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, 1254999271 + ... + 1254999929.

Almost surely, 2^827044736400 is an apocalyptic number.

827044736400 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

827044736400 is the 909420-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 827044736400

827044736400 is an abundant number, since it is smaller than the sum of its proper divisors (2177801269489).

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

827044736400 is a wasteful number, since it uses less digits than its factorization.

827044736400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1388 (or 692 counting only the distinct ones).

The product of its (nonzero) digits is 903168, while the sum is 45.

The spelling of 827044736400 in words is "eight hundred twenty-seven billion, forty-four million, seven hundred thirty-six thousand, four hundred".