137772 has 36 divisors (see below), whose sum is σ = 360360. Its totient is φ = 44352.

The previous prime is 137771. The next prime is 137777. The reversal of 137772 is 277731.

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

It is a super-2 number, since 2×137772² = 37962247968, which contains 22 as substring.

It is an Ulam number.

It is a plaindrome in base 7.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 137772.

It is not an unprimeable number, because it can be changed into a prime (137771) 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, 1504 + ... + 1592.

It is an arithmetic number, because the mean of its divisors is an integer number (10010).

137772 is a Friedman number, since it can be written as (7+2)*(7*3^7-1), using all its digits and the basic arithmetic operations.

2¹³⁷⁷⁷² is an apocalyptic number.

137772 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 137772, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (180180).

137772 is an abundant number, since it is smaller than the sum of its proper divisors (222588).

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

137772 is a wasteful number, since it uses less digits than its factorization.

137772 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 142 (or 137 counting only the distinct ones).

The product of its digits is 2058, while the sum is 27.

The square root of 137772 is about 371.1765078773. The cubic root of 137772 is about 51.6480173183.

It can be divided in two parts, 137 and 772, that added together give a palindrome (909).

The spelling of 137772 in words is "one hundred thirty-seven thousand, seven hundred seventy-two".