3409406208000 has 1536 divisors, whose sum is σ = 14295258432000. Its totient is φ = 794669875200.

The previous prime is 3409406207887. The next prime is 3409406208049. The reversal of 3409406208000 is 8026049043.

It is a happy number.

3409406208000 is a `hidden beast` number, since 3 + 40 + 9 + 406 + 208 + 0 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1536).

It is a super-3 number, since 3×3409406208000³ (a number of 39 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

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

It is an unprimeable number.

It is a polite number, since it can be written in 127 ways as a sum of consecutive naturals, for example, 1707263002 + ... + 1707264998.

It is an arithmetic number, because the mean of its divisors is an integer number (9306808875).

Almost surely, 2^{3409406208000} is an apocalyptic number.

3409406208000 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 3409406208000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (7147629216000).

3409406208000 is an abundant number, since it is smaller than the sum of its proper divisors (10885852224000).

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

3409406208000 is a wasteful number, since it uses less digits than its factorization.

3409406208000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2075 (or 2039 counting only the distinct ones).

The product of its (nonzero) digits is 41472, while the sum is 36.

The spelling of 3409406208000 in words is "three trillion, four hundred nine billion, four hundred six million, two hundred eight thousand".