82753200 has 180 divisors, whose sum is σ = 291036928. Its totient is φ = 21772800.

The previous prime is 82753183. The next prime is 82753207. The reversal of 82753200 is 235728.

It is a tau number, because it is divible by the number of its divisors (180).

It is a super-2 number, since 2×82753200² = 13696184220480000, which contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (82753207) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 457110 + ... + 457290.

Almost surely, 2^82753200 is an apocalyptic number.

82753200 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 82753200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (145518464).

82753200 is an abundant number, since it is smaller than the sum of its proper divisors (208283728).

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

82753200 is a wasteful number, since it uses less digits than its factorization.

82753200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 332 (or 318 counting only the distinct ones).

The product of its (nonzero) digits is 3360, while the sum is 27.

The square root of 82753200 is about 9096.8785855369. The cubic root of 82753200 is about 435.7742848743.

Adding to 82753200 its reverse (235728), we get a palindrome (82988928).

The spelling of 82753200 in words is "eighty-two million, seven hundred fifty-three thousand, two hundred".