827729510400 has 1296 divisors, whose sum is σ = 3407640897024. Its totient is φ = 190253629440.

The previous prime is 827729510359. The next prime is 827729510407. The reversal of 827729510400 is 4015927728.

It is a happy number.

827729510400 is a `hidden beast` number, since 8 + 2 + 77 + 29 + 510 + 40 + 0 = 666.

It is a super-2 number, since 2×827729510400² (a number of 25 digits) contains 22 as substring.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (827729510407) by changing a digit.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 6517555137 + ... + 6517555263.

It is an arithmetic number, because the mean of its divisors is an integer number (2629352544).

Almost surely, 2^827729510400 is an apocalyptic number.

827729510400 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 827729510400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1703820448512).

827729510400 is an abundant number, since it is smaller than the sum of its proper divisors (2579911386624).

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

827729510400 is a wasteful number, since it uses less digits than its factorization.

827729510400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 207 (or 167 counting only the distinct ones).

The product of its (nonzero) digits is 282240, while the sum is 45.

The spelling of 827729510400 in words is "eight hundred twenty-seven billion, seven hundred twenty-nine million, five hundred ten thousand, four hundred".