82464000 has 144 divisors (see below), whose sum is σ = 274223040. Its totient is φ = 21964800.

The previous prime is 82463987. The next prime is 82464001. The reversal of 82464000 is 46428.

It is a super-2 number, since 2×82464000² = 13600622592000000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82464001) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 95571 + ... + 96429.

Almost surely, 2^82464000 is an apocalyptic number.

82464000 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 82464000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (137111520).

82464000 is an abundant number, since it is smaller than the sum of its proper divisors (191759040).

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

82464000 is an equidigital number, since it uses as much as digits as its factorization.

82464000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 893 (or 869 counting only the distinct ones).

The product of its (nonzero) digits is 1536, while the sum is 24.

The square root of 82464000 is about 9080.9691112788. The cubic root of 82464000 is about 435.2660547084.

It can be divided in two parts, 8246 and 4000, that added together give a triangular number (12246 = T₁₅₆).

The spelling of 82464000 in words is "eighty-two million, four hundred sixty-four thousand".