138824400 has 240 divisors, whose sum is σ = 523091520. Its totient is φ = 31027200.

The previous prime is 138824381. The next prime is 138824447. The reversal of 138824400 is 4428831.

It is a tau number, because it is divible by the number of its divisors (240).

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 171196 + ... + 172004.

It is an arithmetic number, because the mean of its divisors is an integer number (2179548).

Almost surely, 2^138824400 is an apocalyptic number.

138824400 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 138824400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (261545760).

138824400 is an abundant number, since it is smaller than the sum of its proper divisors (384267120).

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

138824400 is a wasteful number, since it uses less digits than its factorization.

138824400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 854 (or 843 counting only the distinct ones).

The product of its (nonzero) digits is 6144, while the sum is 30.

The square root of 138824400 is about 11782.3766702648. The cubic root of 138824400 is about 517.7919191282.

The spelling of 138824400 in words is "one hundred thirty-eight million, eight hundred twenty-four thousand, four hundred".