34561382400 has 576 divisors, whose sum is σ = 132591513600. Its totient is φ = 8807546880.

The previous prime is 34561382399. The next prime is 34561382419. The reversal of 34561382400 is 428316543.

34561382400 is a `hidden beast` number, since 34 + 5 + 613 + 8 + 2 + 4 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (576).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 31794657 + ... + 31795743.

It is an arithmetic number, because the mean of its divisors is an integer number (230193600).

Almost surely, 2^34561382400 is an apocalyptic number.

34561382400 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 34561382400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (66295756800).

34561382400 is an abundant number, since it is smaller than the sum of its proper divisors (98030131200).

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

34561382400 is a wasteful number, since it uses less digits than its factorization.

34561382400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1151 (or 1120 counting only the distinct ones).

The product of its (nonzero) digits is 69120, while the sum is 36.

Adding to 34561382400 its reverse (428316543), we get a palindrome (34989698943).

It can be divided in two parts, 3456 and 1382400, that multiplied together give a square (4777574400 = 69120²).

The spelling of 34561382400 in words is "thirty-four billion, five hundred sixty-one million, three hundred eighty-two thousand, four hundred".