What are the divisors of 2669?

1, 17, 157, 2669

There is a total of 4 positive divisors.
The sum of these divisors is 2844.
The arithmetic mean is 711.

4 odd divisors

1, 17, 157, 2669

How to compute the divisors of 2669?

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 2669 by each of the numbers from 1 to 2669 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)

2669 / 1 = 2669 (the remainder is 0, so 1 is a divisor of 2669)
2669 / 2 = 1334.5 (the remainder is 1, so 2 is not a divisor of 2669)
2669 / 3 = 889.66666666667 (the remainder is 2, so 3 is not a divisor of 2669)
...
2669 / 2668 = 1.0003748125937 (the remainder is 1, so 2668 is not a divisor of 2669)
2669 / 2669 = 1 (the remainder is 0, so 2669 is a divisor of 2669)

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 2669 (i.e. 51.662365412358). 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 $\frac{N}{d} = D$ )

2669 / 1 = 2669 (the remainder is 0, so 1 and 2669 are divisors of 2669)
2669 / 2 = 1334.5 (the remainder is 1, so 2 is not a divisor of 2669)
2669 / 3 = 889.66666666667 (the remainder is 2, so 3 is not a divisor of 2669)
...
2669 / 50 = 53.38 (the remainder is 19, so 50 is not a divisor of 2669)
2669 / 51 = 52.333333333333 (the remainder is 17, so 51 is not a divisor of 2669)