82977882624 has 840 divisors, whose sum is σ = 312296222700. Its totient is φ = 21821571072.

The previous prime is 82977882593. The next prime is 82977882629. The reversal of 82977882624 is 42628877928.

82977882624 is a `hidden beast` number, since 8 + 297 + 7 + 88 + 262 + 4 = 666.

It can be written as a sum of positive squares in 2 ways, for example, as 82529798400 + 448084224 = 287280^2 + 21168^2 .

It is a super-4 number, since 4×82977882624⁴ (a number of 45 digits) contains 4444 as substring. Note that it is a super-d number also for d = 2.

It is a Harshad number since it is a multiple of its sum of digits (63).

It is a nude number because it is divisible by every one of its digits.

It is not an unprimeable number, because it can be changed into a prime (82977882629) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 83 ways as a sum of consecutive naturals, for example, 237758802 + ... + 237759150.

Almost surely, 2^82977882624 is an apocalyptic number.

82977882624 is a gapful number since it is divisible by the number (84) 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 82977882624, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (156148111350).

82977882624 is an abundant number, since it is smaller than the sum of its proper divisors (229318340076).

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

82977882624 is an equidigital number, since it uses as much as digits as its factorization.

82977882624 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 412 (or 374 counting only the distinct ones).

The product of its digits is 43352064, while the sum is 63.

The spelling of 82977882624 in words is "eighty-two billion, nine hundred seventy-seven million, eight hundred eighty-two thousand, six hundred twenty-four".