824320000 has 280 divisors, whose sum is σ = 2456663616. Its totient is φ = 270336000.

The previous prime is 824319949. The next prime is 824320009. The reversal of 824320000 is 23428.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (280).

It is a hoax number, since the sum of its digits (19) coincides with the sum of the digits of its distinct prime factors.

It is a self number, because there is not a number n which added to its sum of digits gives 824320000.

It is not an unprimeable number, because it can be changed into a prime (824320009) by changing a digit.

It is a polite number, since it can be written in 19 ways as a sum of consecutive naturals, for example, 35839989 + ... + 35840011.

Almost surely, 2^824320000 is an apocalyptic number.

824320000 is a gapful number since it is divisible by the number (80) 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 824320000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1228331808).

824320000 is an abundant number, since it is smaller than the sum of its proper divisors (1632343616).

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

824320000 is an frugal number, since it uses more digits than its factorization.

824320000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 76 (or 37 counting only the distinct ones).

The product of its (nonzero) digits is 384, while the sum is 19.

The square root of 824320000 is about 28710.9735118822. The cubic root of 824320000 is about 937.6309742939.

Adding to 824320000 its reverse (23428), we get a palindrome (824343428).

The spelling of 824320000 in words is "eight hundred twenty-four million, three hundred twenty thousand".