506188800 has 396 divisors, whose sum is σ = 1963359580. Its totient is φ = 124600320.

The previous prime is 506188769. The next prime is 506188817. The reversal of 506188800 is 8881605.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It can be written as a sum of positive squares in 6 ways, for example, as 410305536 + 95883264 = 20256^2 + 9792^2 .

It is a super-3 number, since 3×506188800³ (a number of 27 digits) contains 333 as substring.

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 35 ways as a sum of consecutive naturals, for example, 38937594 + ... + 38937606.

Almost surely, 2^506188800 is an apocalyptic number.

506188800 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 506188800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (981679790).

506188800 is an abundant number, since it is smaller than the sum of its proper divisors (1457170780).

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

506188800 is a wasteful number, since it uses less digits than its factorization.

506188800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 75 (or 23 counting only the distinct ones).

The product of its (nonzero) digits is 15360, while the sum is 36.

The square root of 506188800 is about 22498.6399588953. The cubic root of 506188800 is about 796.9618096893.

The spelling of 506188800 in words is "five hundred six million, one hundred eighty-eight thousand, eight hundred".