What are the divisors of 3123?

1, 3, 9, 347, 1041, 3123

There is a total of 6 positive divisors.
The sum of these divisors is 4524.
The arithmetic mean is 754.

6 odd divisors

1, 3, 9, 347, 1041, 3123

How to compute the divisors of 3123?

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 3123 by each of the numbers from 1 to 3123 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)

3123 / 1 = 3123 (the remainder is 0, so 1 is a divisor of 3123)
3123 / 2 = 1561.5 (the remainder is 1, so 2 is not a divisor of 3123)
3123 / 3 = 1041 (the remainder is 0, so 3 is a divisor of 3123)
...
3123 / 3122 = 1.0003203074952 (the remainder is 1, so 3122 is not a divisor of 3123)
3123 / 3123 = 1 (the remainder is 0, so 3123 is a divisor of 3123)

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 3123 (i.e. 55.883808030591). 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 $\frac{N}{d} = D$ )

3123 / 1 = 3123 (the remainder is 0, so 1 and 3123 are divisors of 3123)
3123 / 2 = 1561.5 (the remainder is 1, so 2 is not a divisor of 3123)
3123 / 3 = 1041 (the remainder is 0, so 3 and 1041 are divisors of 3123)
...
3123 / 54 = 57.833333333333 (the remainder is 45, so 54 is not a divisor of 3123)
3123 / 55 = 56.781818181818 (the remainder is 43, so 55 is not a divisor of 3123)