82848000 has 144 divisors (see below), whose sum is σ = 275498496. Its totient is φ = 22067200.

The previous prime is 82847993. The next prime is 82848013. The reversal of 82848000 is 84828.

It is a super-2 number, since 2×82848000² = 13727582208000000, which contains 22 as substring.

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

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 95569 + ... + 96431.

It is an arithmetic number, because the mean of its divisors is an integer number (1913184).

Almost surely, 2^82848000 is an apocalyptic number.

82848000 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 82848000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (137749248).

82848000 is an abundant number, since it is smaller than the sum of its proper divisors (192650496).

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

82848000 is an equidigital number, since it uses as much as digits as its factorization.

82848000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 897 (or 873 counting only the distinct ones).

The product of its (nonzero) digits is 4096, while the sum is 30.

The square root of 82848000 is about 9102.0876726167. The cubic root of 82848000 is about 435.9406254192.

It can be divided in two parts, 828 and 48000, that added together give a triangular number (48828 = T₃₁₂).

The spelling of 82848000 in words is "eighty-two million, eight hundred forty-eight thousand".