677606400 has 396 divisors, whose sum is σ = 2583715212. Its totient is φ = 169082880.

The previous prime is 677606399. The next prime is 677606407. The reversal of 677606400 is 4606776.

677606400 is a `hidden beast` number, since 6 + 7 + 7 + 6 + 0 + 640 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 40144896 + 637461504 = 6336^2 + 25248^2 .

It is a super-3 number, since 3×677606400³ (a number of 27 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (677606407) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 3916714 + ... + 3916886.

Almost surely, 2^677606400 is an apocalyptic number.

677606400 is a gapful number since it is divisible by the number (60) 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 677606400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1291857606).

677606400 is an abundant number, since it is smaller than the sum of its proper divisors (1906108812).

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

677606400 is a wasteful number, since it uses less digits than its factorization.

677606400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 226 (or 200 counting only the distinct ones).

The product of its (nonzero) digits is 42336, while the sum is 36.

The square root of 677606400 is about 26030.8739768760. The cubic root of 677606400 is about 878.3329320627.

The spelling of 677606400 in words is "six hundred seventy-seven million, six hundred six thousand, four hundred".