What are the divisors of 3169?

1, 3169

There is a total of 2 positive divisors.
The sum of these divisors is 3170.
The arithmetic mean is 1585.

2 odd divisors

1, 3169

How to compute the divisors of 3169?

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 3169 by each of the numbers from 1 to 3169 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)

3169 / 1 = 3169 (the remainder is 0, so 1 is a divisor of 3169)
3169 / 2 = 1584.5 (the remainder is 1, so 2 is not a divisor of 3169)
3169 / 3 = 1056.3333333333 (the remainder is 1, so 3 is not a divisor of 3169)
...
3169 / 3168 = 1.0003156565657 (the remainder is 1, so 3168 is not a divisor of 3169)
3169 / 3169 = 1 (the remainder is 0, so 3169 is a divisor of 3169)

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 3169 (i.e. 56.29387178015). 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 $\frac{N}{d} = D$ )

3169 / 1 = 3169 (the remainder is 0, so 1 and 3169 are divisors of 3169)
3169 / 2 = 1584.5 (the remainder is 1, so 2 is not a divisor of 3169)
3169 / 3 = 1056.3333333333 (the remainder is 1, so 3 is not a divisor of 3169)
...
3169 / 55 = 57.618181818182 (the remainder is 34, so 55 is not a divisor of 3169)
3169 / 56 = 56.589285714286 (the remainder is 33, so 56 is not a divisor of 3169)