34448970816000 has 3360 divisors, whose sum is σ = 148239415806768. Its totient is φ = 7949883801600.

The previous prime is 34448970815999. The next prime is 34448970816011. The reversal of 34448970816000 is 61807984443.

34448970816000 is a `hidden beast` number, since 34 + 4 + 489 + 70 + 8 + 1 + 60 + 0 + 0 = 666.

It can be written as a sum of positive squares in 24 ways, for example, as 8450230397184 + 25998740418816 = 2906928^2 + 5098896^2 .

It is a Harshad number since it is a multiple of its sum of digits (54).

It is an unprimeable number.

It is a polite number, since it can be written in 335 ways as a sum of consecutive naturals, for example, 134042687872 + ... + 134042688128.

Almost surely, 2^{34448970816000} is an apocalyptic number.

34448970816000 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 34448970816000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (74119707903384).

34448970816000 is an abundant number, since it is smaller than the sum of its proper divisors (113790444990768).

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

34448970816000 is an equidigital number, since it uses as much as digits as its factorization.

34448970816000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 351 (or 297 counting only the distinct ones).

The product of its (nonzero) digits is 4644864, while the sum is 54.

The spelling of 34448970816000 in words is "thirty-four trillion, four hundred forty-eight billion, nine hundred seventy million, eight hundred sixteen thousand".