38768400 has 270 divisors, whose sum is σ = 149541210. Its totient is φ = 9292800.

The previous prime is 38768393. The next prime is 38768419. The reversal of 38768400 is 486783.

It can be written as a sum of positive squares in 3 ways, for example, as 278784 + 38489616 = 528^2 + 6204^2 .

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a polite number, since it can be written in 53 ways as a sum of consecutive naturals, for example, 435556 + ... + 435644.

Almost surely, 2^38768400 is an apocalyptic number.

38768400 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 38768400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (74770605).

38768400 is an abundant number, since it is smaller than the sum of its proper divisors (110772810).

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

38768400 is a wasteful number, since it uses less digits than its factorization.

38768400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 135 (or 110 counting only the distinct ones).

The product of its (nonzero) digits is 32256, while the sum is 36.

The square root of 38768400 is about 6226.4275471574. The cubic root of 38768400 is about 338.4485251407.

The spelling of 38768400 in words is "thirty-eight million, seven hundred sixty-eight thousand, four hundred".