349776000 has 384 divisors, whose sum is σ = 1439717760. Its totient is φ = 79718400.

The previous prime is 349775981. The next prime is 349776001. The reversal of 349776000 is 677943.

349776000 is a `hidden beast` number, since 3 + 49 + 7 + 7 + 600 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (384).

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

It is not an unprimeable number, because it can be changed into a prime (349776001) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1007827 + ... + 1008173.

It is an arithmetic number, because the mean of its divisors is an integer number (3749265).

Almost surely, 2^349776000 is an apocalyptic number.

349776000 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 349776000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (719858880).

349776000 is an abundant number, since it is smaller than the sum of its proper divisors (1089941760).

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

349776000 is a wasteful number, since it uses less digits than its factorization.

349776000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 389 (or 364 counting only the distinct ones).

The product of its (nonzero) digits is 31752, while the sum is 36.

The square root of 349776000 is about 18702.2993238799. The cubic root of 349776000 is about 704.5794987491.

It can be divided in two parts, 3497 and 76000, that added together give a palindrome (79497).

The spelling of 349776000 in words is "three hundred forty-nine million, seven hundred seventy-six thousand".