478224000 has 448 divisors, whose sum is σ = 1826140680. Its totient is φ = 124416000.

The previous prime is 478223987. The next prime is 478224017. The reversal of 478224000 is 422874.

It can be written as a sum of positive squares in 4 ways, for example, as 39237696 + 438986304 = 6264^2 + 20952^2 .

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 55 ways as a sum of consecutive naturals, for example, 11663980 + ... + 11664020.

Almost surely, 2^478224000 is an apocalyptic number.

478224000 is a gapful number since it is divisible by the number (40) 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 478224000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (913070340).

478224000 is an abundant number, since it is smaller than the sum of its proper divisors (1347916680).

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

478224000 is an frugal number, since it uses more digits than its factorization.

478224000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 88 (or 51 counting only the distinct ones).

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

The square root of 478224000 is about 21868.3332698219. Note that the first 3 decimals coincide. The cubic root of 478224000 is about 782.0066674384.

Adding to 478224000 its reverse (422874), we get a palindrome (478646874).

It can be divided in two parts, 4782 and 24000, that added together give a palindrome (28782).

The spelling of 478224000 in words is "four hundred seventy-eight million, two hundred twenty-four thousand".