361584000 has 448 divisors, whose sum is σ = 1391345280. Its totient is φ = 93312000.

The previous prime is 361583983. The next prime is 361584001. The reversal of 361584000 is 485163.

361584000 is a `hidden beast` number, since 3 + 615 + 8 + 40 + 0 + 0 = 666.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (361584001) by changing a digit.

It is a polite number, since it can be written in 55 ways as a sum of consecutive naturals, for example, 11663985 + ... + 11664015.

Almost surely, 2^361584000 is an apocalyptic number.

361584000 is a gapful number since it is divisible by the number (30) 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 361584000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (695672640).

361584000 is an abundant number, since it is smaller than the sum of its proper divisors (1029761280).

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

361584000 is an frugal number, since it uses more digits than its factorization.

361584000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 78 (or 41 counting only the distinct ones).

The product of its (nonzero) digits is 2880, while the sum is 27.

The square root of 361584000 is about 19015.3622105917. The cubic root of 361584000 is about 712.4204897425.

The spelling of 361584000 in words is "three hundred sixty-one million, five hundred eighty-four thousand".