34400123200 has 126 divisors (see below), whose sum is σ = 89336821326. Its totient is φ = 13035617280.

The previous prime is 34400123189. The next prime is 34400123207. The reversal of 34400123200 is 232100443.

It can be written as a sum of positive squares in 3 ways, for example, as 349540416 + 34050582784 = 18696^2 + 184528^2 .

It is a Harshad number since it is a multiple of its sum of digits (19).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (34400123207) by changing a digit.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 547822 + ... + 607378.

Almost surely, 2^34400123200 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 34400123200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (44668410663).

34400123200 is an abundant number, since it is smaller than the sum of its proper divisors (54936698126).

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

34400123200 is a wasteful number, since it uses less digits than its factorization.

34400123200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 59617 (or 59583 counting only the distinct ones).

The product of its (nonzero) digits is 576, while the sum is 19.

Adding to 34400123200 its reverse (232100443), we get a palindrome (34632223643).

The spelling of 34400123200 in words is "thirty-four billion, four hundred million, one hundred twenty-three thousand, two hundred".