137972 has 12 divisors (see below), whose sum is σ = 255780. Its totient is φ = 64896.

The previous prime is 137957. The next prime is 137983. The reversal of 137972 is 279731.

It is a happy number.

137972 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 2 ways, for example, as 126736 + 11236 = 356^2 + 106^2 .

It is a congruent number.

It is an unprimeable number.

137972 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 947 + ... + 1082.

It is an arithmetic number, because the mean of its divisors is an integer number (21315).

2¹³⁷⁹⁷² is an apocalyptic number.

It is an amenable number.

137972 is a deficient number, since it is larger than the sum of its proper divisors (117808).

137972 is a wasteful number, since it uses less digits than its factorization.

137972 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2050 (or 2048 counting only the distinct ones).

The product of its digits is 2646, while the sum is 29.

The square root of 137972 is about 371.4458237752. The cubic root of 137972 is about 51.6729972588.

It can be divided in two parts, 1 and 37972, that added together give a palindrome (37973).

The spelling of 137972 in words is "one hundred thirty-seven thousand, nine hundred seventy-two".