224032000 has 72 divisors (see below), whose sum is σ = 558171432. Its totient is φ = 89600000.

The previous prime is 224031991. The next prime is 224032013. The reversal of 224032000 is 230422.

It can be written as a sum of positive squares in 4 ways, for example, as 13897984 + 210134016 = 3728^2 + 14496^2 .

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 28500 + ... + 35500.

It is an arithmetic number, because the mean of its divisors is an integer number (7752381).

Almost surely, 2^224032000 is an apocalyptic number.

224032000 is a gapful number since it is divisible by the number (20) 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 224032000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (279085716).

224032000 is an abundant number, since it is smaller than the sum of its proper divisors (334139432).

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

224032000 is an frugal number, since it uses more digits than its factorization.

224032000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 7032 (or 7008 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 13.

The square root of 224032000 is about 14967.6985538860. The cubic root of 224032000 is about 607.3467128931.

Adding to 224032000 its reverse (230422), we get a palindrome (224262422).

The spelling of 224032000 in words is "two hundred twenty-four million, thirty-two thousand".