807505920 has 312 divisors, whose sum is σ = 3023265336. Its totient is φ = 198180864.

The previous prime is 807505849. The next prime is 807505931. The reversal of 807505920 is 29505708.

It can be written as a sum of positive squares in 4 ways, for example, as 36864 + 807469056 = 192^2 + 28416^2 .

It is a tau number, because it is divible by the number of its divisors (312).

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 23 ways as a sum of consecutive naturals, for example, 2395992 + ... + 2396328.

It is an arithmetic number, because the mean of its divisors is an integer number (9689953).

Almost surely, 2^807505920 is an apocalyptic number.

807505920 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 807505920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1511632668).

807505920 is an abundant number, since it is smaller than the sum of its proper divisors (2215759416).

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

807505920 is a wasteful number, since it uses less digits than its factorization.

807505920 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 385 (or 360 counting only the distinct ones).

The product of its (nonzero) digits is 25200, while the sum is 36.

The square root of 807505920 is about 28416.6486412455. The cubic root of 807505920 is about 931.2120167082.

The spelling of 807505920 in words is "eight hundred seven million, five hundred five thousand, nine hundred twenty".