3456406800 has 720 divisors, whose sum is σ = 15404168832. Its totient is φ = 696729600.

The previous prime is 3456406777. The next prime is 3456406801. The reversal of 3456406800 is 86046543.

3456406800 is a `hidden beast` number, since 3 + 4 + 5 + 640 + 6 + 8 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (720).

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 (3456406801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 10256232 + ... + 10256568.

Almost surely, 2^3456406800 is an apocalyptic number.

3456406800 is a gapful number since it is divisible by the number (30) 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 3456406800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (7702084416).

3456406800 is an abundant number, since it is smaller than the sum of its proper divisors (11947762032).

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

3456406800 is a wasteful number, since it uses less digits than its factorization.

3456406800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 416 (or 402 counting only the distinct ones).

The product of its (nonzero) digits is 69120, while the sum is 36.

The square root of 3456406800 is about 58791.2136292491. The cubic root of 3456406800 is about 1511.9645788292.

The spelling of 3456406800 in words is "three billion, four hundred fifty-six million, four hundred six thousand, eight hundred".