What are the divisors of 3179?

1, 11, 17, 187, 289, 3179

There is a total of 6 positive divisors.
The sum of these divisors is 3684.
The arithmetic mean is 614.

6 odd divisors

1, 11, 17, 187, 289, 3179

How to compute the divisors of 3179?

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 3179 by each of the numbers from 1 to 3179 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)

3179 / 1 = 3179 (the remainder is 0, so 1 is a divisor of 3179)
3179 / 2 = 1589.5 (the remainder is 1, so 2 is not a divisor of 3179)
3179 / 3 = 1059.6666666667 (the remainder is 2, so 3 is not a divisor of 3179)
...
3179 / 3178 = 1.0003146633103 (the remainder is 1, so 3178 is not a divisor of 3179)
3179 / 3179 = 1 (the remainder is 0, so 3179 is a divisor of 3179)

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 3179 (i.e. 56.382621436042). 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 $\frac{N}{d} = D$ )

3179 / 1 = 3179 (the remainder is 0, so 1 and 3179 are divisors of 3179)
3179 / 2 = 1589.5 (the remainder is 1, so 2 is not a divisor of 3179)
3179 / 3 = 1059.6666666667 (the remainder is 2, so 3 is not a divisor of 3179)
...
3179 / 55 = 57.8 (the remainder is 44, so 55 is not a divisor of 3179)
3179 / 56 = 56.767857142857 (the remainder is 43, so 56 is not a divisor of 3179)