61564800 has 288 divisors, whose sum is σ = 227094840. Its totient is φ = 14643200.

The previous prime is 61564793. The next prime is 61564801. The reversal of 61564800 is 846516.

61564800 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a super-3 number, since 3×61564800³ (a number of 24 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (61564801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 1161574 + ... + 1161626.

Almost surely, 2^61564800 is an apocalyptic number.

61564800 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 61564800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (113547420).

61564800 is an abundant number, since it is smaller than the sum of its proper divisors (165530040).

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

61564800 is a wasteful number, since it uses less digits than its factorization.

61564800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 102 (or 74 counting only the distinct ones).

The product of its (nonzero) digits is 5760, while the sum is 30.

The square root of 61564800 is about 7846.3239800559. The cubic root of 61564800 is about 394.8609241731.

The spelling of 61564800 in words is "sixty-one million, five hundred sixty-four thousand, eight hundred".