What are the divisors of 2667?

1, 3, 7, 21, 127, 381, 889, 2667

There is a total of 8 positive divisors.
The sum of these divisors is 4096.
The arithmetic mean is 512.

8 odd divisors

1, 3, 7, 21, 127, 381, 889, 2667

How to compute the divisors of 2667?

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 2667 by each of the numbers from 1 to 2667 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)

2667 / 1 = 2667 (the remainder is 0, so 1 is a divisor of 2667)
2667 / 2 = 1333.5 (the remainder is 1, so 2 is not a divisor of 2667)
2667 / 3 = 889 (the remainder is 0, so 3 is a divisor of 2667)
...
2667 / 2666 = 1.0003750937734 (the remainder is 1, so 2666 is not a divisor of 2667)
2667 / 2667 = 1 (the remainder is 0, so 2667 is a divisor of 2667)

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 2667 (i.e. 51.643005334701). 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 $\frac{N}{d} = D$ )

2667 / 1 = 2667 (the remainder is 0, so 1 and 2667 are divisors of 2667)
2667 / 2 = 1333.5 (the remainder is 1, so 2 is not a divisor of 2667)
2667 / 3 = 889 (the remainder is 0, so 3 and 889 are divisors of 2667)
...
2667 / 50 = 53.34 (the remainder is 17, so 50 is not a divisor of 2667)
2667 / 51 = 52.294117647059 (the remainder is 15, so 51 is not a divisor of 2667)