What are the divisors of 1060?

1, 2, 4, 5, 10, 20, 53, 106, 212, 265, 530, 1060

There is a total of 12 positive divisors.
The sum of these divisors is 2268.
The arithmetic mean is 189.

8 even divisors

2, 4, 10, 20, 106, 212, 530, 1060

4 odd divisors

1, 5, 53, 265

How to compute the divisors of 1060?

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 1060 by each of the numbers from 1 to 1060 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)

1060 / 1 = 1060 (the remainder is 0, so 1 is a divisor of 1060)
1060 / 2 = 530 (the remainder is 0, so 2 is a divisor of 1060)
1060 / 3 = 353.33333333333 (the remainder is 1, so 3 is not a divisor of 1060)
...
1060 / 1059 = 1.0009442870633 (the remainder is 1, so 1059 is not a divisor of 1060)
1060 / 1060 = 1 (the remainder is 0, so 1060 is a divisor of 1060)

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 1060 (i.e. 32.557641192199). 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 $\frac{N}{d} = D$ )

1060 / 1 = 1060 (the remainder is 0, so 1 and 1060 are divisors of 1060)
1060 / 2 = 530 (the remainder is 0, so 2 and 530 are divisors of 1060)
1060 / 3 = 353.33333333333 (the remainder is 1, so 3 is not a divisor of 1060)
...
1060 / 31 = 34.193548387097 (the remainder is 6, so 31 is not a divisor of 1060)
1060 / 32 = 33.125 (the remainder is 4, so 32 is not a divisor of 1060)