82735200 has 108 divisors (see below), whose sum is σ = 291770388. Its totient is φ = 22060800.

The previous prime is 82735189. The next prime is 82735223. The reversal of 82735200 is 253728.

It is a super-2 number, since 2×82735200² = 13690226638080000, which contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 1455 + ... + 12945.

Almost surely, 2^82735200 is an apocalyptic number.

82735200 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 82735200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (145885194).

82735200 is an abundant number, since it is smaller than the sum of its proper divisors (209035188).

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

82735200 is a wasteful number, since it uses less digits than its factorization.

82735200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 11517 (or 11501 counting only the distinct ones).

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

The square root of 82735200 is about 9095.8891813830. The cubic root of 82735200 is about 435.7426868780.

Adding to 82735200 its reverse (253728), we get a palindrome (82988928).

The spelling of 82735200 in words is "eighty-two million, seven hundred thirty-five thousand, two hundred".