506202400 has 288 divisors, whose sum is σ = 1464656256. Its totient is φ = 168960000.

The previous prime is 506202373. The next prime is 506202409. The reversal of 506202400 is 4202605.

It is not an unprimeable number, because it can be changed into a prime (506202409) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 8298370 + ... + 8298430.

It is an arithmetic number, because the mean of its divisors is an integer number (5085612).

Almost surely, 2^506202400 is an apocalyptic number.

506202400 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 506202400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (732328128).

506202400 is an abundant number, since it is smaller than the sum of its proper divisors (958453856).

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

506202400 is a wasteful number, since it uses less digits than its factorization.

506202400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 156 (or 143 counting only the distinct ones).

The product of its (nonzero) digits is 480, while the sum is 19.

The square root of 506202400 is about 22498.9421973567. The cubic root of 506202400 is about 796.9689470680.

It can be divided in two parts, 506 and 202400, that multiplied together give a square (102414400 = 10120²).

The spelling of 506202400 in words is "five hundred six million, two hundred two thousand, four hundred".