34540405977600 has 720 divisors, whose sum is σ = 124996217397480. Its totient is φ = 9107767296000.

The previous prime is 34540405977503. The next prime is 34540405977601. The reversal of 34540405977600 is 677950404543.

34540405977600 is a `hidden beast` number, since 3 + 4 + 5 + 4 + 0 + 40 + 597 + 7 + 6 + 0 + 0 = 666.

It can be written as a sum of positive squares in 12 ways, for example, as 3789033543936 + 30751372433664 = 1946544^2 + 5545392^2 .

It is a tau number, because it is divible by the number of its divisors (720).

It is not an unprimeable number, because it can be changed into a prime (34540405977601) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 12438027412 + ... + 12438030188.

Almost surely, 2^{34540405977600} is an apocalyptic number.

34540405977600 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 34540405977600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (62498108698740).

34540405977600 is an abundant number, since it is smaller than the sum of its proper divisors (90455811419880).

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

34540405977600 is a wasteful number, since it uses less digits than its factorization.

34540405977600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3981 (or 3957 counting only the distinct ones).

The product of its (nonzero) digits is 12700800, while the sum is 54.

The spelling of 34540405977600 in words is "thirty-four trillion, five hundred forty billion, four hundred five million, nine hundred seventy-seven thousand, six hundred".