349516800 has 396 divisors, whose sum is σ = 1316605836. Its totient is φ = 88473600.

The previous prime is 349516733. The next prime is 349516807. The reversal of 349516800 is 8615943.

349516800 is a `hidden beast` number, since 3 + 495 + 168 + 0 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 13307904 + 336208896 = 3648^2 + 18336^2 .

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (349516807) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 8524780 + ... + 8524820.

Almost surely, 2^349516800 is an apocalyptic number.

349516800 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 349516800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (658302918).

349516800 is an abundant number, since it is smaller than the sum of its proper divisors (967089036).

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

349516800 is a wasteful number, since it uses less digits than its factorization.

349516800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 114 (or 88 counting only the distinct ones).

The product of its (nonzero) digits is 25920, while the sum is 36.

The square root of 349516800 is about 18695.3684103844. The cubic root of 349516800 is about 704.4054138716.

The spelling of 349516800 in words is "three hundred forty-nine million, five hundred sixteen thousand, eight hundred".