766886400 has 480 divisors, whose sum is σ = 3227114880. Its totient is φ = 174735360.

The previous prime is 766886387. The next prime is 766886429. The reversal of 766886400 is 4688667.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (480).

It is a super-2 number, since 2×766886400² = 1176229501009920000, which contains 22 as substring.

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 47 ways as a sum of consecutive naturals, for example, 2419042 + ... + 2419358.

It is an arithmetic number, because the mean of its divisors is an integer number (6723156).

Almost surely, 2^766886400 is an apocalyptic number.

766886400 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 766886400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1613557440).

766886400 is an abundant number, since it is smaller than the sum of its proper divisors (2460228480).

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

766886400 is a wasteful number, since it uses less digits than its factorization.

766886400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 361 (or 334 counting only the distinct ones).

The product of its (nonzero) digits is 387072, while the sum is 45.

The square root of 766886400 is about 27692.7138431754. The cubic root of 766886400 is about 915.3285570953.

The spelling of 766886400 in words is "seven hundred sixty-six million, eight hundred eighty-six thousand, four hundred".