What are the divisors of 5169?

1, 3, 1723, 5169

There is a total of 4 positive divisors.
The sum of these divisors is 6896.
The arithmetic mean is 1724.

4 odd divisors

1, 3, 1723, 5169

How to compute the divisors of 5169?

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 5169 by each of the numbers from 1 to 5169 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)

5169 / 1 = 5169 (the remainder is 0, so 1 is a divisor of 5169)
5169 / 2 = 2584.5 (the remainder is 1, so 2 is not a divisor of 5169)
5169 / 3 = 1723 (the remainder is 0, so 3 is a divisor of 5169)
...
5169 / 5168 = 1.000193498452 (the remainder is 1, so 5168 is not a divisor of 5169)
5169 / 5169 = 1 (the remainder is 0, so 5169 is a divisor of 5169)

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 5169 (i.e. 71.895757872075). 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 $\frac{N}{d} = D$ )

5169 / 1 = 5169 (the remainder is 0, so 1 and 5169 are divisors of 5169)
5169 / 2 = 2584.5 (the remainder is 1, so 2 is not a divisor of 5169)
5169 / 3 = 1723 (the remainder is 0, so 3 and 1723 are divisors of 5169)
...
5169 / 70 = 73.842857142857 (the remainder is 59, so 70 is not a divisor of 5169)
5169 / 71 = 72.802816901408 (the remainder is 57, so 71 is not a divisor of 5169)