20180 has 12 divisors (see below), whose sum is σ = 42420. Its totient is φ = 8064.

The previous prime is 20177. The next prime is 20183. The reversal of 20180 is 8102.

20180 = T₇₉ + T₈₀ + ... + T₈₄.

It is an interprime number because it is at equal distance from previous prime (20177) and next prime (20183).

It can be written as a sum of positive squares in 2 ways, for example, as 6724 + 13456 = 82^2 + 116^2 .

20180 is a modest number, since divided by 180 gives 20 as remainder.

It is a plaindrome in base 7.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (20183) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 485 + ... + 524.

It is an arithmetic number, because the mean of its divisors is an integer number (3535).

2²⁰¹⁸⁰ is an apocalyptic number.

20180 is a gapful number since it is divisible by the number (20) formed by its first and last digit.

It is an amenable number.

20180 is an abundant number, since it is smaller than the sum of its proper divisors (22240).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (21210).

20180 is a wasteful number, since it uses less digits than its factorization.

20180 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1018 (or 1016 counting only the distinct ones).

The product of its (nonzero) digits is 16, while the sum is 11.

The square root of 20180 is about 142.0563268566. The cubic root of 20180 is about 27.2253656111.

Subtracting from 20180 its product of nonzero digits (16), we obtain a square (20164 = 142²).

Adding to 20180 its reverse (8102), we get a palindrome (28282).

It can be divided in two parts, 20 and 180, that multiplied together give a square (3600 = 60²).

The spelling of 20180 in words is "twenty thousand, one hundred eighty".