What are the divisors of 2692?

1, 2, 4, 673, 1346, 2692

There is a total of 6 positive divisors.
The sum of these divisors is 4718.
The arithmetic mean is 786.33333333333.

4 even divisors

2, 4, 1346, 2692

2 odd divisors

1, 673

How to compute the divisors of 2692?

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 2692 by each of the numbers from 1 to 2692 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)

2692 / 1 = 2692 (the remainder is 0, so 1 is a divisor of 2692)
2692 / 2 = 1346 (the remainder is 0, so 2 is a divisor of 2692)
2692 / 3 = 897.33333333333 (the remainder is 1, so 3 is not a divisor of 2692)
...
2692 / 2691 = 1.0003716090673 (the remainder is 1, so 2691 is not a divisor of 2692)
2692 / 2692 = 1 (the remainder is 0, so 2692 is a divisor of 2692)

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 2692 (i.e. 51.884487084291). 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 $\frac{N}{d} = D$ )

2692 / 1 = 2692 (the remainder is 0, so 1 and 2692 are divisors of 2692)
2692 / 2 = 1346 (the remainder is 0, so 2 and 1346 are divisors of 2692)
2692 / 3 = 897.33333333333 (the remainder is 1, so 3 is not a divisor of 2692)
...
2692 / 50 = 53.84 (the remainder is 42, so 50 is not a divisor of 2692)
2692 / 51 = 52.78431372549 (the remainder is 40, so 51 is not a divisor of 2692)