What are the divisors of 7079?

1, 7079

There is a total of 2 positive divisors.
The sum of these divisors is 7080.
The arithmetic mean is 3540.

2 odd divisors

1, 7079

How to compute the divisors of 7079?

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 7079 by each of the numbers from 1 to 7079 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)

7079 / 1 = 7079 (the remainder is 0, so 1 is a divisor of 7079)
7079 / 2 = 3539.5 (the remainder is 1, so 2 is not a divisor of 7079)
7079 / 3 = 2359.6666666667 (the remainder is 2, so 3 is not a divisor of 7079)
...
7079 / 7078 = 1.0001412828483 (the remainder is 1, so 7078 is not a divisor of 7079)
7079 / 7079 = 1 (the remainder is 0, so 7079 is a divisor of 7079)

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 7079 (i.e. 84.136793378403). 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 $\frac{N}{d} = D$ )

7079 / 1 = 7079 (the remainder is 0, so 1 and 7079 are divisors of 7079)
7079 / 2 = 3539.5 (the remainder is 1, so 2 is not a divisor of 7079)
7079 / 3 = 2359.6666666667 (the remainder is 2, so 3 is not a divisor of 7079)
...
7079 / 83 = 85.289156626506 (the remainder is 24, so 83 is not a divisor of 7079)
7079 / 84 = 84.27380952381 (the remainder is 23, so 84 is not a divisor of 7079)