What are the divisors of 2148?

1, 2, 3, 4, 6, 12, 179, 358, 537, 716, 1074, 2148

There is a total of 12 positive divisors.
The sum of these divisors is 5040.
The arithmetic mean is 420.

8 even divisors

2, 4, 6, 12, 358, 716, 1074, 2148

4 odd divisors

1, 3, 179, 537

How to compute the divisors of 2148?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 2148 by each of the numbers from 1 to 2148 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

2148 / 1 = 2148 (the remainder is 0, so 1 is a divisor of 2148)
2148 / 2 = 1074 (the remainder is 0, so 2 is a divisor of 2148)
2148 / 3 = 716 (the remainder is 0, so 3 is a divisor of 2148)
...
2148 / 2147 = 1.0004657661854 (the remainder is 1, so 2147 is not a divisor of 2148)
2148 / 2148 = 1 (the remainder is 0, so 2148 is a divisor of 2148)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 2148 (i.e. 46.346520905026). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

2148 / 1 = 2148 (the remainder is 0, so 1 and 2148 are divisors of 2148)
2148 / 2 = 1074 (the remainder is 0, so 2 and 1074 are divisors of 2148)
2148 / 3 = 716 (the remainder is 0, so 3 and 716 are divisors of 2148)
...
2148 / 45 = 47.733333333333 (the remainder is 33, so 45 is not a divisor of 2148)
2148 / 46 = 46.695652173913 (the remainder is 32, so 46 is not a divisor of 2148)