513788000 has 96 divisors (see below), whose sum is σ = 1377256608. Its totient is φ = 186816000.

The previous prime is 513787997. The next prime is 513788003. The reversal of 513788000 is 887315.

It is an interprime number because it is at equal distance from previous prime (513787997) and next prime (513788003).

It is a Harshad number since it is a multiple of its sum of digits (32).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513788003) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 38162 + ... + 49838.

It is an arithmetic number, because the mean of its divisors is an integer number (14346423).

Almost surely, 2^513788000 is an apocalyptic number.

513788000 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 513788000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (688628304).

513788000 is an abundant number, since it is smaller than the sum of its proper divisors (863468608).

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

513788000 is a wasteful number, since it uses less digits than its factorization.

513788000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 11713 (or 11695 counting only the distinct ones).

The product of its (nonzero) digits is 6720, while the sum is 32.

The square root of 513788000 is about 22666.8921557412. The cubic root of 513788000 is about 800.9301680651.

The spelling of 513788000 in words is "five hundred thirteen million, seven hundred eighty-eight thousand".