What are the divisors of 2612?

1, 2, 4, 653, 1306, 2612

There is a total of 6 positive divisors.
The sum of these divisors is 4578.
The arithmetic mean is 763.

4 even divisors

2, 4, 1306, 2612

2 odd divisors

1, 653

How to compute the divisors of 2612?

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 2612 by each of the numbers from 1 to 2612 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)

2612 / 1 = 2612 (the remainder is 0, so 1 is a divisor of 2612)
2612 / 2 = 1306 (the remainder is 0, so 2 is a divisor of 2612)
2612 / 3 = 870.66666666667 (the remainder is 2, so 3 is not a divisor of 2612)
...
2612 / 2611 = 1.0003829950211 (the remainder is 1, so 2611 is not a divisor of 2612)
2612 / 2612 = 1 (the remainder is 0, so 2612 is a divisor of 2612)

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 2612 (i.e. 51.107729356723). 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 $\frac{N}{d} = D$ )

2612 / 1 = 2612 (the remainder is 0, so 1 and 2612 are divisors of 2612)
2612 / 2 = 1306 (the remainder is 0, so 2 and 1306 are divisors of 2612)
2612 / 3 = 870.66666666667 (the remainder is 2, so 3 is not a divisor of 2612)
...
2612 / 50 = 52.24 (the remainder is 12, so 50 is not a divisor of 2612)
2612 / 51 = 51.21568627451 (the remainder is 11, so 51 is not a divisor of 2612)