827405107200 has 1008 divisors, whose sum is σ = 3495027970560. Its totient is φ = 187988705280.

The previous prime is 827405107159. The next prime is 827405107229. The reversal of 827405107200 is 2701504728.

827405107200 is a `hidden beast` number, since 8 + 2 + 74 + 0 + 510 + 72 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1008).

It is a super-2 number, since 2×827405107200² (a number of 25 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 4954521517 + ... + 4954521683.

Almost surely, 2^827405107200 is an apocalyptic number.

827405107200 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 827405107200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1747513985280).

827405107200 is an abundant number, since it is smaller than the sum of its proper divisors (2667622863360).

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

827405107200 is an frugal number, since it uses more digits than its factorization.

827405107200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 233 (or 184 counting only the distinct ones).

The product of its (nonzero) digits is 31360, while the sum is 36.

The spelling of 827405107200 in words is "eight hundred twenty-seven billion, four hundred five million, one hundred seven thousand, two hundred".