205142137200 has 2160 divisors, whose sum is σ = 1000815229440. Its totient is φ = 37739520000.

The previous prime is 205142137147. The next prime is 205142137259. The reversal of 205142137200 is 2731241502.

205142137200 is a `hidden beast` number, since 2 + 0 + 5 + 1 + 421 + 37 + 200 = 666.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 431 ways as a sum of consecutive naturals, for example, 1358557125 + ... + 1358557275.

It is an arithmetic number, because the mean of its divisors is an integer number (463340384).

Almost surely, 2^205142137200 is an apocalyptic number.

205142137200 is a gapful number since it is divisible by the number (20) 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 205142137200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (500407614720).

205142137200 is an abundant number, since it is smaller than the sum of its proper divisors (795673092240).

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

205142137200 is a wasteful number, since it uses less digits than its factorization.

205142137200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 248 (or 221 counting only the distinct ones).

The product of its (nonzero) digits is 3360, while the sum is 27.

Adding to 205142137200 its reverse (2731241502), we get a palindrome (207873378702).

The spelling of 205142137200 in words is "two hundred five billion, one hundred forty-two million, one hundred thirty-seven thousand, two hundred".