338406916393728 has 1728 divisors, whose sum is σ = 1330248608640000. Its totient is φ = 84550896009216.

The previous prime is 338406916393687. The next prime is 338406916393757. The reversal of 338406916393728 is 827393619604833.

338406916393728 is a `hidden beast` number, since 3 + 3 + 8 + 406 + 9 + 1 + 63 + 93 + 72 + 8 = 666.

It is a tau number, because it is divible by the number of its divisors (1728).

It is a super-2 number, since 2×338406916393728² (a number of 30 digits) contains 22 as substring.

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

It is an unprimeable number.

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 191 ways as a sum of consecutive naturals, for example, 7612667950 + ... + 7612712402.

Almost surely, 2^{338406916393728} is an apocalyptic number.

338406916393728 is a gapful number since it is divisible by the number (38) 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 338406916393728, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (665124304320000).

338406916393728 is an abundant number, since it is smaller than the sum of its proper divisors (991841692246272).

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

338406916393728 is a wasteful number, since it uses less digits than its factorization.

338406916393728 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 44544 (or 44497 counting only the distinct ones).

The product of its (nonzero) digits is 846526464, while the sum is 72.

The spelling of 338406916393728 in words is "three hundred thirty-eight trillion, four hundred six billion, nine hundred sixteen million, three hundred ninety-three thousand, seven hundred twenty-eight".