138045600 has 576 divisors, whose sum is σ = 629959680. Its totient is φ = 28339200.

The previous prime is 138045599. The next prime is 138045601. The reversal of 138045600 is 6540831.

138045600 = 76³ + 77³ + ... + 155³.

138045600 is a `hidden beast` number, since 13 + 8 + 0 + 45 + 600 = 666.

It is an interprime number because it is at equal distance from previous prime (138045599) and next prime (138045601).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is not an unprimeable number, because it can be changed into a prime (138045601) by changing a digit.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 1663159 + ... + 1663241.

It is an arithmetic number, because the mean of its divisors is an integer number (1093680).

Almost surely, 2^138045600 is an apocalyptic number.

138045600 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 138045600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (314979840).

138045600 is an abundant number, since it is smaller than the sum of its proper divisors (491914080).

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

138045600 is a wasteful number, since it uses less digits than its factorization.

138045600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 130 (or 111 counting only the distinct ones).

The product of its (nonzero) digits is 2880, while the sum is 27.

The square root of 138045600 is about 11749.2808290550. The cubic root of 138045600 is about 516.8218380034.

The spelling of 138045600 in words is "one hundred thirty-eight million, forty-five thousand, six hundred".