34090826400 has 360 divisors, whose sum is σ = 125082361404. Its totient is φ = 9035366400.

The previous prime is 34090826369. The next prime is 34090826401. The reversal of 34090826400 is 462809043.

It is a happy number.

34090826400 is a `hidden beast` number, since 3 + 4 + 0 + 9 + 0 + 8 + 2 + 640 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 29698318224 + 4392508176 = 172332^2 + 66276^2 .

It is a tau number, because it is divible by the number of its divisors (360).

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 (34090826401) by changing a digit.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 11208880 + ... + 11211920.

Almost surely, 2^34090826400 is an apocalyptic number.

34090826400 is a gapful number since it is divisible by the number (30) formed by its first and last digit.

34090826400 is the 116775-th heptagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 34090826400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (62541180702).

34090826400 is an abundant number, since it is smaller than the sum of its proper divisors (90991535004).

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

34090826400 is a wasteful number, since it uses less digits than its factorization.

34090826400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3246 (or 3224 counting only the distinct ones).

The product of its (nonzero) digits is 41472, while the sum is 36.

The spelling of 34090826400 in words is "thirty-four billion, ninety million, eight hundred twenty-six thousand, four hundred".