What are the divisors of 2172?

1, 2, 3, 4, 6, 12, 181, 362, 543, 724, 1086, 2172

There is a total of 12 positive divisors.
The sum of these divisors is 5096.
The arithmetic mean is 424.66666666667.

8 even divisors

2, 4, 6, 12, 362, 724, 1086, 2172

4 odd divisors

1, 3, 181, 543

How to compute the divisors of 2172?

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 2172 by each of the numbers from 1 to 2172 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)

2172 / 1 = 2172 (the remainder is 0, so 1 is a divisor of 2172)
2172 / 2 = 1086 (the remainder is 0, so 2 is a divisor of 2172)
2172 / 3 = 724 (the remainder is 0, so 3 is a divisor of 2172)
...
2172 / 2171 = 1.0004606172271 (the remainder is 1, so 2171 is not a divisor of 2172)
2172 / 2172 = 1 (the remainder is 0, so 2172 is a divisor of 2172)

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 2172 (i.e. 46.604720790924). 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 $\frac{N}{d} = D$ )

2172 / 1 = 2172 (the remainder is 0, so 1 and 2172 are divisors of 2172)
2172 / 2 = 1086 (the remainder is 0, so 2 and 1086 are divisors of 2172)
2172 / 3 = 724 (the remainder is 0, so 3 and 724 are divisors of 2172)
...
2172 / 45 = 48.266666666667 (the remainder is 12, so 45 is not a divisor of 2172)
2172 / 46 = 47.217391304348 (the remainder is 10, so 46 is not a divisor of 2172)