82355200 has 66 divisors (see below), whose sum is σ = 204204626. Its totient is φ = 32931840.

The previous prime is 82355197. The next prime is 82355213. The reversal of 82355200 is 255328.

It can be written as a sum of positive squares in 3 ways, for example, as 17842176 + 64513024 = 4224^2 + 8032^2 .

It is a Harshad number since it is a multiple of its sum of digits (25).

It is an unprimeable number.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 23992 + ... + 27208.

Almost surely, 2^82355200 is an apocalyptic number.

82355200 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 82355200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (102102313).

82355200 is an abundant number, since it is smaller than the sum of its proper divisors (121849426).

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

82355200 is a wasteful number, since it uses less digits than its factorization.

82355200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3247 (or 3224 counting only the distinct ones).

The product of its (nonzero) digits is 2400, while the sum is 25.

The square root of 82355200 is about 9074.9765839918. The cubic root of 82355200 is about 435.0745457306.

The spelling of 82355200 in words is "eighty-two million, three hundred fifty-five thousand, two hundred".