What are the divisors of 1079?

1, 13, 83, 1079

There is a total of 4 positive divisors.
The sum of these divisors is 1176.
The arithmetic mean is 294.

4 odd divisors

1, 13, 83, 1079

How to compute the divisors of 1079?

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 1079 by each of the numbers from 1 to 1079 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)

1079 / 1 = 1079 (the remainder is 0, so 1 is a divisor of 1079)
1079 / 2 = 539.5 (the remainder is 1, so 2 is not a divisor of 1079)
1079 / 3 = 359.66666666667 (the remainder is 2, so 3 is not a divisor of 1079)
...
1079 / 1078 = 1.0009276437848 (the remainder is 1, so 1078 is not a divisor of 1079)
1079 / 1079 = 1 (the remainder is 0, so 1079 is a divisor of 1079)

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 1079 (i.e. 32.848135411314). 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 $\frac{N}{d} = D$ )

1079 / 1 = 1079 (the remainder is 0, so 1 and 1079 are divisors of 1079)
1079 / 2 = 539.5 (the remainder is 1, so 2 is not a divisor of 1079)
1079 / 3 = 359.66666666667 (the remainder is 2, so 3 is not a divisor of 1079)
...
1079 / 31 = 34.806451612903 (the remainder is 25, so 31 is not a divisor of 1079)
1079 / 32 = 33.71875 (the remainder is 23, so 32 is not a divisor of 1079)