768398400 has 945 divisors, whose sum is σ = 3611414037. Its totient is φ = 159667200.

The previous prime is 768398383. The next prime is 768398431. The reversal of 768398400 is 4893867.

It is a happy number.

The square root of 768398400 is 27720.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in only one way, i.e., 276623424 + 491774976 = 16632^2 + 22176^2 .

It is a tau number, because it is divible by the number of its divisors (945).

It is a super-2 number, since 2×768398400² = 1180872202245120000, 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 pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 134 ways as a sum of consecutive naturals, for example, 69854395 + ... + 69854405.

Almost surely, 2^768398400 is an apocalyptic number.

768398400 is a gapful number since it is divisible by the number (70) formed by its first and last digit.

768398400 is the 27720-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 768398400

768398400 is an abundant number, since it is smaller than the sum of its proper divisors (2843015637).

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

768398400 is a wasteful number, since it uses less digits than its factorization.

768398400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 70 (or 28 counting only the distinct ones).

The product of its (nonzero) digits is 290304, while the sum is 45.

The cubic root of 768398400 is about 915.9297188057.

The spelling of 768398400 in words is "seven hundred sixty-eight million, three hundred ninety-eight thousand, four hundred".