349584076800 has 1248 divisors, whose sum is σ = 1492486696960. Its totient is φ = 79546613760.

The previous prime is 349584076763. The next prime is 349584076813. The reversal of 349584076800 is 8670485943.

349584076800 is a `hidden beast` number, since 3 + 495 + 8 + 4 + 0 + 76 + 80 + 0 = 666.

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 95 ways as a sum of consecutive naturals, for example, 1567641489 + ... + 1567641711.

Almost surely, 2^349584076800 is an apocalyptic number.

349584076800 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 349584076800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (746243348480).

349584076800 is an abundant number, since it is smaller than the sum of its proper divisors (1142902620160).

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

349584076800 is an frugal number, since it uses more digits than its factorization.

349584076800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 285 (or 240 counting only the distinct ones).

The product of its (nonzero) digits is 5806080, while the sum is 54.

The spelling of 349584076800 in words is "three hundred forty-nine billion, five hundred eighty-four million, seventy-six thousand, eight hundred".