117972 has 36 divisors (see below), whose sum is σ = 311220. Its totient is φ = 37632.

The previous prime is 117959. The next prime is 117973. The reversal of 117972 is 279711.

It can be written as a sum of positive squares in 2 ways, for example, as 24336 + 93636 = 156^2 + 306^2 .

It is a tau number, because it is divible by the number of its divisors (36).

Its product of digits (882) is a multiple of the sum of its prime divisors (147).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (117973) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 988 + ... + 1100.

It is an arithmetic number, because the mean of its divisors is an integer number (8645).

2¹¹⁷⁹⁷² is an apocalyptic number.

117972 is a gapful number since it is divisible by the number (12) 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 117972, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (155610).

117972 is an abundant number, since it is smaller than the sum of its proper divisors (193248).

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

117972 is a wasteful number, since it uses less digits than its factorization.

117972 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 152 (or 147 counting only the distinct ones).

The product of its digits is 882, while the sum is 27.

The square root of 117972 is about 343.4705227527. The cubic root of 117972 is about 49.0448014516.

It can be divided in two parts, 117 and 972, that added together give a square (1089 = 33²).

The spelling of 117972 in words is "one hundred seventeen thousand, nine hundred seventy-two".