61584364800 has 648 divisors, whose sum is σ = 260997836736. Its totient is φ = 14073937920.

The previous prime is 61584364769. The next prime is 61584364801. The reversal of 61584364800 is 846348516.

61584364800 is a `hidden beast` number, since 6 + 1 + 584 + 3 + 64 + 8 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (648).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (61584364801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 10883572 + ... + 10889228.

Almost surely, 2^61584364800 is an apocalyptic number.

61584364800 is a gapful number since it is divisible by the number (60) 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 61584364800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (130498918368).

61584364800 is an abundant number, since it is smaller than the sum of its proper divisors (199413471936).

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

61584364800 is an equidigital number, since it uses as much as digits as its factorization.

61584364800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5705 (or 5674 counting only the distinct ones).

The product of its (nonzero) digits is 552960, while the sum is 45.

The spelling of 61584364800 in words is "sixty-one billion, five hundred eighty-four million, three hundred sixty-four thousand, eight hundred".