38765317392400 has 135 divisors (see below), whose sum is σ = 93676809351909. Its totient is φ = 15416220917760.

The previous prime is 38765317392397. The next prime is 38765317392401. The reversal of 38765317392400 is 429371356783.

The square root of 38765317392400 is 6226180.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in 13 ways, for example, as 29891019383824 + 8874298008576 = 5467268^2 + 2978976^2 .

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (38765317392401) by changing a digit.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 24033053994 + ... + 24033055606.

It is a 1-persistent number, because it is pandigital, but 2⋅38765317392400 = 77530634784800 is not.

Almost surely, 2^{38765317392400} is an apocalyptic number.

38765317392400 is the 6226180-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 38765317392400

38765317392400 is an abundant number, since it is smaller than the sum of its proper divisors (54911491959509).

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

38765317392400 is an frugal number, since it uses more digits than its factorization.

38765317392400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3630 (or 1813 counting only the distinct ones).

The product of its (nonzero) digits is 22861440, while the sum is 58.

The spelling of 38765317392400 in words is "thirty-eight trillion, seven hundred sixty-five billion, three hundred seventeen million, three hundred ninety-two thousand, four hundred".