10135785600 has 288 divisors, whose sum is σ = 38072377200. Its totient is φ = 2560481280.

The previous prime is 10135785533. The next prime is 10135785601. The reversal of 10135785600 is 658753101.

10135785600 is a `hidden beast` number, since 10 + 1 + 35 + 7 + 8 + 5 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (10135785601) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 537939 + ... + 556461.

Almost surely, 2^10135785600 is an apocalyptic number.

10135785600 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 10135785600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (19036188600).

10135785600 is an abundant number, since it is smaller than the sum of its proper divisors (27936591600).

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

10135785600 is a wasteful number, since it uses less digits than its factorization.

10135785600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 18572 (or 18552 counting only the distinct ones).

The product of its (nonzero) digits is 25200, while the sum is 36.

The spelling of 10135785600 in words is "ten billion, one hundred thirty-five million, seven hundred eighty-five thousand, six hundred".