What are the divisors of 5079?

1, 3, 1693, 5079

There is a total of 4 positive divisors.
The sum of these divisors is 6776.
The arithmetic mean is 1694.

4 odd divisors

1, 3, 1693, 5079

How to compute the divisors of 5079?

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 5079 by each of the numbers from 1 to 5079 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)

5079 / 1 = 5079 (the remainder is 0, so 1 is a divisor of 5079)
5079 / 2 = 2539.5 (the remainder is 1, so 2 is not a divisor of 5079)
5079 / 3 = 1693 (the remainder is 0, so 3 is a divisor of 5079)
...
5079 / 5078 = 1.0001969279244 (the remainder is 1, so 5078 is not a divisor of 5079)
5079 / 5079 = 1 (the remainder is 0, so 5079 is a divisor of 5079)

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 5079 (i.e. 71.267103210387). 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 $\frac{N}{d} = D$ )

5079 / 1 = 5079 (the remainder is 0, so 1 and 5079 are divisors of 5079)
5079 / 2 = 2539.5 (the remainder is 1, so 2 is not a divisor of 5079)
5079 / 3 = 1693 (the remainder is 0, so 3 and 1693 are divisors of 5079)
...
5079 / 70 = 72.557142857143 (the remainder is 39, so 70 is not a divisor of 5079)
5079 / 71 = 71.535211267606 (the remainder is 38, so 71 is not a divisor of 5079)