513326400 has 168 divisors, whose sum is σ = 1695114720. Its totient is φ = 135997440.

The previous prime is 513326393. The next prime is 513326417. The reversal of 513326400 is 4623315.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1098967 + ... + 1099433.

Almost surely, 2^513326400 is an apocalyptic number.

513326400 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 513326400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (847557360).

513326400 is an abundant number, since it is smaller than the sum of its proper divisors (1181788320).

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

513326400 is a wasteful number, since it uses less digits than its factorization.

513326400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 721 (or 706 counting only the distinct ones).

The product of its (nonzero) digits is 2160, while the sum is 24.

The square root of 513326400 is about 22656.7076160681. The cubic root of 513326400 is about 800.6902376271.

Adding to 513326400 its reverse (4623315), we get a palindrome (517949715).

The spelling of 513326400 in words is "five hundred thirteen million, three hundred twenty-six thousand, four hundred".