What are the divisors of 3130?

1, 2, 5, 10, 313, 626, 1565, 3130

There is a total of 8 positive divisors.
The sum of these divisors is 5652.
The arithmetic mean is 706.5.

4 even divisors

2, 10, 626, 3130

4 odd divisors

1, 5, 313, 1565

How to compute the divisors of 3130?

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 3130 by each of the numbers from 1 to 3130 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)

3130 / 1 = 3130 (the remainder is 0, so 1 is a divisor of 3130)
3130 / 2 = 1565 (the remainder is 0, so 2 is a divisor of 3130)
3130 / 3 = 1043.3333333333 (the remainder is 1, so 3 is not a divisor of 3130)
...
3130 / 3129 = 1.0003195909236 (the remainder is 1, so 3129 is not a divisor of 3130)
3130 / 3130 = 1 (the remainder is 0, so 3130 is a divisor of 3130)

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 3130 (i.e. 55.946402922797). 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 $\frac{N}{d} = D$ )

3130 / 1 = 3130 (the remainder is 0, so 1 and 3130 are divisors of 3130)
3130 / 2 = 1565 (the remainder is 0, so 2 and 1565 are divisors of 3130)
3130 / 3 = 1043.3333333333 (the remainder is 1, so 3 is not a divisor of 3130)
...
3130 / 54 = 57.962962962963 (the remainder is 52, so 54 is not a divisor of 3130)
3130 / 55 = 56.909090909091 (the remainder is 50, so 55 is not a divisor of 3130)