What are the divisors of 2607?

1, 3, 11, 33, 79, 237, 869, 2607

There is a total of 8 positive divisors.
The sum of these divisors is 3840.
The arithmetic mean is 480.

8 odd divisors

1, 3, 11, 33, 79, 237, 869, 2607

How to compute the divisors of 2607?

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 2607 by each of the numbers from 1 to 2607 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)

2607 / 1 = 2607 (the remainder is 0, so 1 is a divisor of 2607)
2607 / 2 = 1303.5 (the remainder is 1, so 2 is not a divisor of 2607)
2607 / 3 = 869 (the remainder is 0, so 3 is a divisor of 2607)
...
2607 / 2606 = 1.0003837298542 (the remainder is 1, so 2606 is not a divisor of 2607)
2607 / 2607 = 1 (the remainder is 0, so 2607 is a divisor of 2607)

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 2607 (i.e. 51.058789644879). 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 $\frac{N}{d} = D$ )

2607 / 1 = 2607 (the remainder is 0, so 1 and 2607 are divisors of 2607)
2607 / 2 = 1303.5 (the remainder is 1, so 2 is not a divisor of 2607)
2607 / 3 = 869 (the remainder is 0, so 3 and 869 are divisors of 2607)
...
2607 / 50 = 52.14 (the remainder is 7, so 50 is not a divisor of 2607)
2607 / 51 = 51.117647058824 (the remainder is 6, so 51 is not a divisor of 2607)