138768400 has 135 divisors (see below), whose sum is σ = 363578013. Its totient is φ = 50889600.

The previous prime is 138768397. The next prime is 138768403. The reversal of 138768400 is 4867831.

It is a happy number.

The square root of 138768400 is 11780.

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

It is an interprime number because it is at equal distance from previous prime (138768397) and next prime (138768403).

It can be written as a sum of positive squares in only one way, i.e., 49956624 + 88811776 = 7068^2 + 9424^2 .

It is a self number, because there is not a number n which added to its sum of digits gives 138768400.

It is not an unprimeable number, because it can be changed into a prime (138768403) 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, 4476385 + ... + 4476415.

Almost surely, 2^138768400 is an apocalyptic number.

138768400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

138768400 is the 11780-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 138768400

138768400 is an abundant number, since it is smaller than the sum of its proper divisors (224809613).

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

138768400 is a wasteful number, since it uses less digits than its factorization.

138768400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 118 (or 57 counting only the distinct ones).

The product of its (nonzero) digits is 32256, while the sum is 37.

The cubic root of 138768400 is about 517.7222862028.

The spelling of 138768400 in words is "one hundred thirty-eight million, seven hundred sixty-eight thousand, four hundred".