765408000 has 576 divisors, whose sum is σ = 3122316288. Its totient is φ = 162201600.

The previous prime is 765407969. The next prime is 765408031. The reversal of 765408000 is 804567.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (765407969) and next prime (765408031).

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 11423967 + ... + 11424033.

It is an arithmetic number, because the mean of its divisors is an integer number (5420688).

Almost surely, 2^765408000 is an apocalyptic number.

765408000 is a gapful number since it is divisible by the number (70) 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 765408000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1561158144).

765408000 is an abundant number, since it is smaller than the sum of its proper divisors (2356908288).

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

765408000 is a wasteful number, since it uses less digits than its factorization.

765408000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 125 (or 101 counting only the distinct ones).

The product of its (nonzero) digits is 6720, while the sum is 30.

The square root of 765408000 is about 27666.0080242886. The cubic root of 765408000 is about 914.7399900231.

The spelling of 765408000 in words is "seven hundred sixty-five million, four hundred eight thousand".