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2538 = 23347

• 25382 = 6441444 is the smallest square that contains exactly five digits '4'.

2538 has 16 divisors (see below), whose sum is σ = 5760. Its totient is φ = 828.

The previous prime is 2531. The next prime is 2539. The reversal of 2538 is 8352.

2538 is digitally balanced in base 5, because in such base it contains all the possibile digits an equal number of times.

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

2538 is strictly pandigital in base 5.

It is a Curzon number.

It is a nialpdrome in base 15.

It is a self number, because there is not a number n which added to its sum of digits gives 2538.

It is not an unprimeable number, because it can be changed into a prime (2531) 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 7 ways as a sum of consecutive naturals, for example, 31 + ... + 77.

It is an arithmetic number, because the mean of its divisors is an integer number (360).

It is a practical number, because each smaller number is the sum of distinct divisors of 2538, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2880).

2538 is an abundant number, since it is smaller than the sum of its proper divisors (3222).

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

2538 is a wasteful number, since it uses less digits than its factorization.

2538 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 58 (or 52 counting only the distinct ones).

The product of its digits is 240, while the sum is 18.

The square root of 2538 is about 50.3785668712. The cubic root of 2538 is about 13.6405078313.

Adding to 2538 its sum of digits (18), we get a triangular number (2556 = T71).

2538 divided by its sum of digits (18) gives a palindrome (141).

The spelling of 2538 in words is "two thousand, five hundred thirty-eight".

Divisors: 1 2 3 6 9 18 27 47 54 94 141 282 423 846 1269 2538