3406838745600 has 1200 divisors, whose sum is σ = 13366603277280. Its totient is φ = 854588620800.

The previous prime is 3406838745599. The next prime is 3406838745659. The reversal of 3406838745600 is 65478386043.

3406838745600 is a `hidden beast` number, since 3 + 4 + 0 + 6 + 8 + 3 + 8 + 74 + 560 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1200).

It is a super-3 number, since 3×3406838745600³ (a number of 39 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is an unprimeable number.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 3210969070 + ... + 3210970130.

Almost surely, 2^{3406838745600} is an apocalyptic number.

3406838745600 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 3406838745600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (6683301638640).

3406838745600 is an abundant number, since it is smaller than the sum of its proper divisors (9959764531680).

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

3406838745600 is a wasteful number, since it uses less digits than its factorization.

3406838745600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1283 (or 1253 counting only the distinct ones).

The product of its (nonzero) digits is 11612160, while the sum is 54.

The spelling of 3406838745600 in words is "three trillion, four hundred six billion, eight hundred thirty-eight million, seven hundred forty-five thousand, six hundred".