198964800 has 252 divisors, whose sum is σ = 726565476. Its totient is φ = 51609600.

The previous prime is 198964783. The next prime is 198964807. The reversal of 198964800 is 8469891.

It can be written as a sum of positive squares in 6 ways, for example, as 53231616 + 145733184 = 7296^2 + 12072^2 .

It is a Harshad number since it is a multiple of its sum of digits (45).

It is not an unprimeable number, because it can be changed into a prime (198964807) 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, 590232 + ... + 590568.

Almost surely, 2^198964800 is an apocalyptic number.

198964800 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 198964800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (363282738).

198964800 is an abundant number, since it is smaller than the sum of its proper divisors (527600676).

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

198964800 is a wasteful number, since it uses less digits than its factorization.

198964800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 406 (or 388 counting only the distinct ones).

The product of its (nonzero) digits is 124416, while the sum is 45.

The square root of 198964800 is about 14105.4882935686. The cubic root of 198964800 is about 583.7928207365.

The spelling of 198964800 in words is "one hundred ninety-eight million, nine hundred sixty-four thousand, eight hundred".