82972120 has 192 divisors, whose sum is σ = 245145600. Its totient is φ = 24710400.

The previous prime is 82972111. The next prime is 82972129. The reversal of 82972120 is 2127928.

It is an interprime number because it is at equal distance from previous prime (82972111) and next prime (82972129).

It is a Harshad number since it is a multiple of its sum of digits (31).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82972129) 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 47 ways as a sum of consecutive naturals, for example, 1050241 + ... + 1050319.

It is an arithmetic number, because the mean of its divisors is an integer number (1276800).

Almost surely, 2^82972120 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 82972120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (122572800).

82972120 is an abundant number, since it is smaller than the sum of its proper divisors (162173480).

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

82972120 is a wasteful number, since it uses less digits than its factorization.

82972120 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 150 (or 135 counting only the distinct ones).

The product of its (nonzero) digits is 4032, while the sum is 31.

The square root of 82972120 is about 9108.9033368458. The cubic root of 82972120 is about 436.1582204990.

The spelling of 82972120 in words is "eighty-two million, nine hundred seventy-two thousand, one hundred twenty".