138624000 has 264 divisors, whose sum is σ = 486661968. Its totient is φ = 35020800.

The previous prime is 138623999. The next prime is 138624011. The reversal of 138624000 is 426831.

It is a happy number.

It is a super-2 number, since 2×138624000² = 38433226752000000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 7295991 + ... + 7296009.

Almost surely, 2^138624000 is an apocalyptic number.

138624000 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 138624000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (243330984).

138624000 is an abundant number, since it is smaller than the sum of its proper divisors (348037968).

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

138624000 is an equidigital number, since it uses as much as digits as its factorization.

138624000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 76 (or 29 counting only the distinct ones).

The product of its (nonzero) digits is 1152, while the sum is 24.

The square root of 138624000 is about 11773.8693724705. The cubic root of 138624000 is about 517.5426462556.

The spelling of 138624000 in words is "one hundred thirty-eight million, six hundred twenty-four thousand".