10006138800 has 360 divisors, whose sum is σ = 42020855136. Its totient is φ = 2152488960.

The previous prime is 10006138789. The next prime is 10006138861. The reversal of 10006138800 is 883160001.

It is a tau number, because it is divible by the number of its divisors (360).

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 416722 + ... + 440078.

Almost surely, 2^10006138800 is an apocalyptic number.

10006138800 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 10006138800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (21010427568).

10006138800 is an abundant number, since it is smaller than the sum of its proper divisors (32014716336).

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

10006138800 is a wasteful number, since it uses less digits than its factorization.

10006138800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 23405 (or 23391 counting only the distinct ones).

The product of its (nonzero) digits is 1152, while the sum is 27.

Adding to 10006138800 its reverse (883160001), we get a palindrome (10889298801).

The spelling of 10006138800 in words is "ten billion, six million, one hundred thirty-eight thousand, eight hundred".