678349904400 has 1215 divisors, whose sum is σ = 2868514444341. Its totient is φ = 148014397440.

The previous prime is 678349904371. The next prime is 678349904459. The reversal of 678349904400 is 4409943876.

It is a happy number.

The square root of 678349904400 is 823620.

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

678349904400 is a `hidden beast` number, since 6 + 78 + 3 + 49 + 90 + 440 + 0 = 666.

It can be written as a sum of positive squares in 13 ways, for example, as 39399074064 + 638950830336 = 198492^2 + 799344^2 .

It is an unprimeable number.

It is a polite number, since it can be written in 242 ways as a sum of consecutive naturals, for example, 12799054774 + ... + 12799054826.

Almost surely, 2^678349904400 is an apocalyptic number.

678349904400 is a gapful number since it is divisible by the number (60) formed by its first and last digit.

678349904400 is the 823620-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 678349904400

678349904400 is an abundant number, since it is smaller than the sum of its proper divisors (2190164539941).

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

678349904400 is a wasteful number, since it uses less digits than its factorization.

678349904400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 218 (or 107 counting only the distinct ones).

The product of its (nonzero) digits is 5225472, while the sum is 54.

The spelling of 678349904400 in words is "six hundred seventy-eight billion, three hundred forty-nine million, nine hundred four thousand, four hundred".