82137968 has 80 divisors (see below), whose sum is σ = 183845376. Its totient is φ = 35185920.

The previous prime is 82137967. The next prime is 82137973. The reversal of 82137968 is 86973128.

It is a Cunningham number, because it is equal to 9063²-1.

It is a Harshad number since it is a multiple of its sum of digits (44).

Its product of digits (145152) is a multiple of the sum of its prime divisors (336).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82137961) 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 15 ways as a sum of consecutive naturals, for example, 416846 + ... + 417042.

Almost surely, 2^82137968 is an apocalyptic number.

82137968 is a gapful number since it is divisible by the number (88) 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 82137968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (91922688).

82137968 is an abundant number, since it is smaller than the sum of its proper divisors (101707408).

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

82137968 is a wasteful number, since it uses less digits than its factorization.

82137968 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 342 (or 336 counting only the distinct ones).

The product of its digits is 145152, while the sum is 44.

The square root of 82137968 is about 9062.9999448306. Note that the first 4 decimals coincide. The cubic root of 82137968 is about 434.6916703513.

The spelling of 82137968 in words is "eighty-two million, one hundred thirty-seven thousand, nine hundred sixty-eight".