824720400 has 240 divisors, whose sum is σ = 3355043200. Its totient is φ = 188490240.

The previous prime is 824720387. The next prime is 824720401. The reversal of 824720400 is 4027428.

It is a tau number, because it is divible by the number of its divisors (240).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is not an unprimeable number, because it can be changed into a prime (824720401) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 70146 + ... + 81054.

Almost surely, 2^824720400 is an apocalyptic number.

824720400 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 824720400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1677521600).

824720400 is an abundant number, since it is smaller than the sum of its proper divisors (2530322800).

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

824720400 is a wasteful number, since it uses less digits than its factorization.

824720400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 10943 (or 10926 counting only the distinct ones).

The product of its (nonzero) digits is 3584, while the sum is 27.

The square root of 824720400 is about 28717.9456089742. The cubic root of 824720400 is about 937.7827627064.

Adding to 824720400 its reverse (4027428), we get a palindrome (828747828).

The spelling of 824720400 in words is "eight hundred twenty-four million, seven hundred twenty thousand, four hundred".