820409163840 has 1008 divisors, whose sum is σ = 3377227696128. Its totient is φ = 182165372928.

The previous prime is 820409163829. The next prime is 820409163851. The reversal of 820409163840 is 48361904028.

It is a happy number.

820409163840 is a `hidden beast` number, since 8 + 2 + 0 + 4 + 0 + 9 + 1 + 638 + 4 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (820409163829) and next prime (820409163851).

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

It is a super-3 number, since 3×820409163840³ (a number of 37 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

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

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 2142060289 + ... + 2142060671.

Almost surely, 2^820409163840 is an apocalyptic number.

820409163840 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 820409163840, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1688613848064).

820409163840 is an abundant number, since it is smaller than the sum of its proper divisors (2556818532288).

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

820409163840 is a wasteful number, since it uses less digits than its factorization.

820409163840 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 816 (or 796 counting only the distinct ones).

The product of its (nonzero) digits is 331776, while the sum is 45.

The spelling of 820409163840 in words is "eight hundred twenty billion, four hundred nine million, one hundred sixty-three thousand, eight hundred forty".