4197128400 has 300 divisors, whose sum is σ = 15149553804. Its totient is φ = 1112832000.

The previous prime is 4197128399. The next prime is 4197128417. The reversal of 4197128400 is 48217914.

4197128400 is a `hidden beast` number, since 41 + 97 + 128 + 400 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 86266944 + 4110861456 = 9288^2 + 64116^2 .

It is a tau number, because it is divible by the number of its divisors (300).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 9104170 + ... + 9104630.

Almost surely, 2^4197128400 is an apocalyptic number.

4197128400 is a gapful number since it is divisible by the number (40) 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 4197128400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (7574776902).

4197128400 is an abundant number, since it is smaller than the sum of its proper divisors (10952425404).

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

4197128400 is a wasteful number, since it uses less digits than its factorization.

4197128400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 772 (or 752 counting only the distinct ones).

The product of its (nonzero) digits is 16128, while the sum is 36.

The square root of 4197128400 is about 64785.2483208948. The cubic root of 4197128400 is about 1613.0608541189.

The spelling of 4197128400 in words is "four billion, one hundred ninety-seven million, one hundred twenty-eight thousand, four hundred".