349648350105600 has 8424 divisors, whose sum is σ = 1754782986596640. Its totient is φ = 68263894056960.

The previous prime is 349648350105559. The next prime is 349648350105617. The reversal of 349648350105600 is 6501053846943.

349648350105600 is a `hidden beast` number, since 3 + 4 + 9 + 6 + 4 + 83 + 501 + 0 + 56 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (8424).

It is a super-3 number, since 3×349648350105600³ (a number of 45 digits) contains 333 as substring.

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 647 ways as a sum of consecutive naturals, for example, 8131356979179 + ... + 8131356979221.

Almost surely, 2^{349648350105600} is an apocalyptic number.

349648350105600 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 349648350105600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (877391493298320).

349648350105600 is an abundant number, since it is smaller than the sum of its proper divisors (1405134636491040).

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

349648350105600 is an equidigital number, since it uses as much as digits as its factorization.

349648350105600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 147 (or 92 counting only the distinct ones).

The product of its (nonzero) digits is 9331200, while the sum is 54.

The spelling of 349648350105600 in words is "three hundred forty-nine trillion, six hundred forty-eight billion, three hundred fifty million, one hundred five thousand, six hundred".