What are the divisors of 3129?

1, 3, 7, 21, 149, 447, 1043, 3129

There is a total of 8 positive divisors.
The sum of these divisors is 4800.
The arithmetic mean is 600.

8 odd divisors

1, 3, 7, 21, 149, 447, 1043, 3129

How to compute the divisors of 3129?

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 3129 by each of the numbers from 1 to 3129 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)

3129 / 1 = 3129 (the remainder is 0, so 1 is a divisor of 3129)
3129 / 2 = 1564.5 (the remainder is 1, so 2 is not a divisor of 3129)
3129 / 3 = 1043 (the remainder is 0, so 3 is a divisor of 3129)
...
3129 / 3128 = 1.0003196930946 (the remainder is 1, so 3128 is not a divisor of 3129)
3129 / 3129 = 1 (the remainder is 0, so 3129 is a divisor of 3129)

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 3129 (i.e. 55.937465083788). 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 $\frac{N}{d} = D$ )

3129 / 1 = 3129 (the remainder is 0, so 1 and 3129 are divisors of 3129)
3129 / 2 = 1564.5 (the remainder is 1, so 2 is not a divisor of 3129)
3129 / 3 = 1043 (the remainder is 0, so 3 and 1043 are divisors of 3129)
...
3129 / 54 = 57.944444444444 (the remainder is 51, so 54 is not a divisor of 3129)
3129 / 55 = 56.890909090909 (the remainder is 49, so 55 is not a divisor of 3129)