138538400 has 288 divisors, whose sum is σ = 456720768. Its totient is φ = 39628800.

The previous prime is 138538391. The next prime is 138538403. The reversal of 138538400 is 4835831.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (32).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (138538403) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 800714 + ... + 800886.

It is an arithmetic number, because the mean of its divisors is an integer number (1585836).

Almost surely, 2^138538400 is an apocalyptic number.

138538400 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 138538400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (228360384).

138538400 is an abundant number, since it is smaller than the sum of its proper divisors (318182368).

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

138538400 is a wasteful number, since it uses less digits than its factorization.

138538400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 224 (or 211 counting only the distinct ones).

The product of its (nonzero) digits is 11520, while the sum is 32.

The square root of 138538400 is about 11770.2336425408. The cubic root of 138538400 is about 517.4360971916.

The spelling of 138538400 in words is "one hundred thirty-eight million, five hundred thirty-eight thousand, four hundred".