34138848764664 has 768 divisors, whose sum is σ = 113978741760000. Its totient is φ = 9041674604544.

The previous prime is 34138848764653. The next prime is 34138848764687. The reversal of 34138848764664 is 46646784883143.

34138848764664 is a `hidden beast` number, since 3 + 4 + 1 + 3 + 8 + 84 + 87 + 6 + 466 + 4 = 666.

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

It is a nude number because it is divisible by every one of its digits.

It is a junction number, because it is equal to n+sod(n) for n = 34138848764592 and 34138848764601.

It is a congruent number.

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, 71271082777 + ... + 71271083255.

It is an arithmetic number, because the mean of its divisors is an integer number (148409820000).

Almost surely, 2^{34138848764664} is an apocalyptic number.

34138848764664 is a gapful number since it is divisible by the number (34) 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 34138848764664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (56989370880000).

34138848764664 is an abundant number, since it is smaller than the sum of its proper divisors (79839892995336).

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

34138848764664 is a wasteful number, since it uses less digits than its factorization.

34138848764664 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 925 (or 884 counting only the distinct ones).

The product of its digits is 1783627776, while the sum is 72.

The spelling of 34138848764664 in words is "thirty-four trillion, one hundred thirty-eight billion, eight hundred forty-eight million, seven hundred sixty-four thousand, six hundred sixty-four".