5209952400 has 225 divisors, whose sum is σ = 18744846043. Its totient is φ = 1385856000.

The previous prime is 5209952393. The next prime is 5209952401. The reversal of 5209952400 is 42599025.

It is a happy number.

The square root of 5209952400 is 72180.

It is a perfect power (a square), and thus also a powerful number.

5209952400 is a `hidden beast` number, since 520 + 9 + 95 + 2 + 40 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 1393678224 + 3816274176 = 37332^2 + 61776^2 .

It is a tau number, because it is divible by the number of its divisors (225).

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

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (5209952401) by changing a digit.

It is a polite number, since it can be written in 44 ways as a sum of consecutive naturals, for example, 12992200 + ... + 12992600.

Almost surely, 2^5209952400 is an apocalyptic number.

5209952400 is a gapful number since it is divisible by the number (50) formed by its first and last digit.

5209952400 is the 72180-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 5209952400

5209952400 is an abundant number, since it is smaller than the sum of its proper divisors (13534893643).

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

5209952400 is an equidigital number, since it uses as much as digits as its factorization.

5209952400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 832 (or 411 counting only the distinct ones).

The product of its (nonzero) digits is 32400, while the sum is 36.

The cubic root of 5209952400 is about 1733.5827829683.

Multiplying 5209952400 by its sum of digits (36), we get a square (187558286400 = 433080²).

5209952400 divided by its sum of digits (36) gives a square (144720900 = 12030²).

Multiplying 5209952400 by its product of nonzero digits (32400), we get a square (168802457760000 = 12992400²).

5209952400 divided by its product of nonzero digits (32400) gives a square (160801 = 401²).

The spelling of 5209952400 in words is "five billion, two hundred nine million, nine hundred fifty-two thousand, four hundred".