72101952 has 84 divisors (see below), whose sum is σ = 222587820. Its totient is φ = 22182912.

The previous prime is 72101951. The next prime is 72101959. The reversal of 72101952 is 25910127.

It can be written as a sum of positive squares in 2 ways, for example, as 46457856 + 25644096 = 6816^2 + 5064^2 .

It is not an unprimeable number, because it can be changed into a prime (72101951) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 2674 + ... + 12302.

It is an arithmetic number, because the mean of its divisors is an integer number (2649855).

Almost surely, 2^72101952 is an apocalyptic number.

72101952 is a gapful number since it is divisible by the number (72) 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 72101952, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (111293910).

72101952 is an abundant number, since it is smaller than the sum of its proper divisors (150485868).

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

72101952 is a wasteful number, since it uses less digits than its factorization.

72101952 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 9660 (or 9647 counting only the distinct ones).

The product of its (nonzero) digits is 1260, while the sum is 27.

The square root of 72101952 is about 8491.2868282729. The cubic root of 72101952 is about 416.2130319142.

The spelling of 72101952 in words is "seventy-two million, one hundred one thousand, nine hundred fifty-two".