83980800 has 270 divisors, whose sum is σ = 312087633. Its totient is φ = 22394880.

The previous prime is 83980789. The next prime is 83980801. The reversal of 83980800 is 808938.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It can be written as a sum of positive squares in 2 ways, for example, as 82301184 + 1679616 = 9072^2 + 1296^2 .

It is a tau number, because it is divible by the number of its divisors (270).

It is an ABA number since it can be written as A⋅B^A, here for A=2, B=6480.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (83980801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 16796158 + ... + 16796162.

Almost surely, 2^83980800 is an apocalyptic number.

83980800 is a gapful number since it is divisible by the number (80) 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 83980800

83980800 is an abundant number, since it is smaller than the sum of its proper divisors (228106833).

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

83980800 is an frugal number, since it uses more digits than its factorization.

83980800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 52 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 13824, while the sum is 36.

The square root of 83980800 is about 9164.1038841777. The cubic root of 83980800 is about 437.9185436813.

The spelling of 83980800 in words is "eighty-three million, nine hundred eighty thousand, eight hundred".