138400 has 36 divisors (see below), whose sum is σ = 339822. Its totient is φ = 55040.

The previous prime is 138389. The next prime is 138401. The reversal of 138400 is 4831.

It can be written as a sum of positive squares in 3 ways, for example, as 126736 + 11664 = 356^2 + 108^2 .

It is a Harshad number since it is a multiple of its sum of digits (16).

It is an Ulam number.

It is not an unprimeable number, because it can be changed into a prime (138401) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 714 + ... + 886.

2¹³⁸⁴⁰⁰ is an apocalyptic number.

138400 is a gapful number since it is divisible by the number (10) 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 138400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (169911).

138400 is an abundant number, since it is smaller than the sum of its proper divisors (201422).

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

138400 is a wasteful number, since it uses less digits than its factorization.

138400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 193 (or 180 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 16.

The square root of 138400 is about 372.0215047548. The cubic root of 138400 is about 51.7263733389.

Subtracting from 138400 its sum of digits (16), we obtain a square (138384 = 372²).

The spelling of 138400 in words is "one hundred thirty-eight thousand, four hundred".