513825000 has 384 divisors, whose sum is σ = 1889879040. Its totient is φ = 115200000.

The previous prime is 513824981. The next prime is 513825007. The reversal of 513825000 is 528315.

It is a super-2 number, since 2×513825000² = 528032261250000000, which contains 22 as substring.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513825007) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 16574985 + ... + 16575015.

It is an arithmetic number, because the mean of its divisors is an integer number (4921560).

Almost surely, 2^513825000 is an apocalyptic number.

513825000 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 513825000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (944939520).

513825000 is an abundant number, since it is smaller than the sum of its proper divisors (1376054040).

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

513825000 is a wasteful number, since it uses less digits than its factorization.

513825000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 95 (or 71 counting only the distinct ones).

The product of its (nonzero) digits is 1200, while the sum is 24.

The square root of 513825000 is about 22667.7083093991. The cubic root of 513825000 is about 800.9493937021.

The spelling of 513825000 in words is "five hundred thirteen million, eight hundred twenty-five thousand".