5102416800 has 504 divisors, whose sum is σ = 20142359244. Its totient is φ = 1254113280.

The previous prime is 5102416799. The next prime is 5102416811. The reversal of 5102416800 is 86142015.

It can be written as a sum of positive squares in 6 ways, for example, as 633226896 + 4469189904 = 25164^2 + 66852^2 .

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 83 ways as a sum of consecutive naturals, for example, 7581264 + ... + 7581936.

Almost surely, 2^5102416800 is an apocalyptic number.

5102416800 is a gapful number since it is divisible by the number (50) 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 5102416800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (10071179622).

5102416800 is an abundant number, since it is smaller than the sum of its proper divisors (15039942444).

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

5102416800 is a wasteful number, since it uses less digits than its factorization.

5102416800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 724 (or 696 counting only the distinct ones).

The product of its (nonzero) digits is 1920, while the sum is 27.

The square root of 5102416800 is about 71431.2032657997. The cubic root of 5102416800 is about 1721.5724757845.

Adding to 5102416800 its reverse (86142015), we get a palindrome (5188558815).

The spelling of 5102416800 in words is "five billion, one hundred two million, four hundred sixteen thousand, eight hundred".