1872 has 30 divisors (see below), whose sum is σ = 5642. Its totient is φ = 576.

The previous prime is 1871. The next prime is 1873. The reversal of 1872 is 2781.

1872 is nontrivially palindromic in base 5.

It is an interprime number because it is at equal distance from previous prime (1871) and next prime (1873).

It can be written as a sum of positive squares in only one way, i.e., 1296 + 576 = 36^2 + 24^2 .

It is a Smith number, since the sum of its digits (18) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an alternating number because its digits alternate between odd and even.

It is a nialpdrome in base 12, base 13 and base 16.

It is a zygodrome in base 12.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 1872.

It is not an unprimeable number, because it can be changed into a prime (1871) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 138 + ... + 150.

1872 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 1872, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2821).

1872 is an abundant number, since it is smaller than the sum of its proper divisors (3770).

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

1872 is a wasteful number, since it uses less digits than its factorization.

1872 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 27 (or 18 counting only the distinct ones).

The product of its digits is 112, while the sum is 18.

The square root of 1872 is about 43.2666153056. The cubic root of 1872 is about 12.3244802955.

Subtracting 1872 from its reverse (2781), we obtain a palindrome (909).

It can be divided in two parts, 18 and 72, that multiplied together give a 4-th power (1296 = 6⁴).

The spelling of 1872 in words is "one thousand, eight hundred seventy-two".