613712000 has 192 divisors, whose sum is σ = 1682455320. Its totient is φ = 222464000.

The previous prime is 613711999. The next prime is 613712003. The reversal of 613712000 is 217316.

It is a happy number.

It can be written as a sum of positive squares in 4 ways, for example, as 53348416 + 560363584 = 7304^2 + 23672^2 .

It is a hoax number, since the sum of its digits (20) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (20).

It is not an unprimeable number, because it can be changed into a prime (613712003) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1935842 + ... + 1936158.

Almost surely, 2^613712000 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 613712000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (841227660).

613712000 is an abundant number, since it is smaller than the sum of its proper divisors (1068743320).

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

613712000 is a wasteful number, since it uses less digits than its factorization.

613712000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 368 (or 335 counting only the distinct ones).

The product of its (nonzero) digits is 252, while the sum is 20.

The square root of 613712000 is about 24773.2113380563. The cubic root of 613712000 is about 849.8094151716.

Adding to 613712000 its reverse (217316), we get a palindrome (613929316).

The spelling of 613712000 in words is "six hundred thirteen million, seven hundred twelve thousand".