4180 has 24 divisors (see below), whose sum is σ = 10080. Its totient is φ = 1440.

The previous prime is 4177. The next prime is 4201. The reversal of 4180 is 814.

4180 is an esthetic number in base 9, because in such base its adjacent digits differ by 1.

It is a plaindrome in base 15.

It is a self number, because there is not a number n which added to its sum of digits gives 4180.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 211 + ... + 229.

It is an arithmetic number, because the mean of its divisors is an integer number (420).

2⁴¹⁸⁰ 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 4180, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (5040).

4180 is an abundant number, since it is smaller than the sum of its proper divisors (5900).

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

4180 is a wasteful number, since it uses less digits than its factorization.

4180 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 39 (or 37 counting only the distinct ones).

The product of its (nonzero) digits is 32, while the sum is 13.

The square root of 4180 is about 64.6529195010. The cubic root of 4180 is about 16.1086357231.

Adding to 4180 its reverse (814), we get a palindrome (4994).

It can be divided in two parts, 41 and 80, that added together give a palindrome (121).

The spelling of 4180 in words is "four thousand, one hundred eighty".