82752000 has 160 divisors (see below), whose sum is σ = 275768064. Its totient is φ = 22016000.

The previous prime is 82751983. The next prime is 82752001. The reversal of 82752000 is 25728.

It is a tau number, because it is divible by the number of its divisors (160).

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 (82752001) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 191785 + ... + 192215.

Almost surely, 2^82752000 is an apocalyptic number.

82752000 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 82752000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (137884032).

82752000 is an abundant number, since it is smaller than the sum of its proper divisors (193016064).

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

82752000 is an equidigital number, since it uses as much as digits as its factorization.

82752000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 467 (or 441 counting only the distinct ones).

The product of its (nonzero) digits is 1120, while the sum is 24.

The square root of 82752000 is about 9096.8126286079. The cubic root of 82752000 is about 435.7721784838.

Adding to 82752000 its reverse (25728), we get a palindrome (82777728).

The spelling of 82752000 in words is "eighty-two million, seven hundred fifty-two thousand".