34609688948016 has 960 divisors, whose sum is σ = 125258097254400. Its totient is φ = 8956290051072.

The previous prime is 34609688947991. The next prime is 34609688948027. The reversal of 34609688948016 is 61084988690643.

34609688948016 is a `hidden beast` number, since 3 + 4 + 6 + 0 + 9 + 68 + 89 + 480 + 1 + 6 = 666.

It is a Harshad number since it is a multiple of its sum of digits (72).

It is an unprimeable number.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 29157277375 + ... + 29157278561.

It is an arithmetic number, because the mean of its divisors is an integer number (130477184640).

Almost surely, 2^{34609688948016} is an apocalyptic number.

34609688948016 is a gapful number since it is divisible by the number (36) 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 34609688948016, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (62629048627200).

34609688948016 is an abundant number, since it is smaller than the sum of its proper divisors (90648408306384).

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

34609688948016 is a wasteful number, since it uses less digits than its factorization.

34609688948016 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2263 (or 2238 counting only the distinct ones).

The product of its (nonzero) digits is 429981696, while the sum is 72.

The spelling of 34609688948016 in words is "thirty-four trillion, six hundred nine billion, six hundred eighty-eight million, nine hundred forty-eight thousand, sixteen".