338417312800 has 576 divisors, whose sum is σ = 999546524928. Its totient is φ = 109486080000.

The previous prime is 338417312797. The next prime is 338417312851. The reversal of 338417312800 is 8213714833.

It is a happy number.

It is a super-3 number, since 3×338417312800³ (a number of 36 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is a Harshad number since it is a multiple of its sum of digits (40).

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 1022408635 + ... + 1022408965.

It is an arithmetic number, because the mean of its divisors is an integer number (1735323828).

Almost surely, 2^338417312800 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 338417312800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (499773262464).

338417312800 is an abundant number, since it is smaller than the sum of its proper divisors (661129212128).

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

338417312800 is a wasteful number, since it uses less digits than its factorization.

338417312800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 533 (or 520 counting only the distinct ones).

The product of its (nonzero) digits is 96768, while the sum is 40.

The spelling of 338417312800 in words is "three hundred thirty-eight billion, four hundred seventeen million, three hundred twelve thousand, eight hundred".