205688100 has 144 divisors (see below), whose sum is σ = 650958336. Its totient is φ = 49920000.

The previous prime is 205688099. The next prime is 205688107. The reversal of 205688100 is 1886502.

It is a super-2 number, since 2×205688100² = 84615188963220000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (205688107) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 157450 + ... + 158750.

It is an arithmetic number, because the mean of its divisors is an integer number (4520544).

Almost surely, 2^205688100 is an apocalyptic number.

205688100 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 205688100, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (325479168).

205688100 is an abundant number, since it is smaller than the sum of its proper divisors (445270236).

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

205688100 is a wasteful number, since it uses less digits than its factorization.

205688100 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1366 (or 1359 counting only the distinct ones).

The product of its (nonzero) digits is 3840, while the sum is 30.

The square root of 205688100 is about 14341.8304271108. The cubic root of 205688100 is about 590.2958393776.

The spelling of 205688100 in words is "two hundred five million, six hundred eighty-eight thousand, one hundred".