What are the divisors of 2693?

1, 2693

There is a total of 2 positive divisors.
The sum of these divisors is 2694.
The arithmetic mean is 1347.

2 odd divisors

1, 2693

How to compute the divisors of 2693?

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 2693 by each of the numbers from 1 to 2693 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)

2693 / 1 = 2693 (the remainder is 0, so 1 is a divisor of 2693)
2693 / 2 = 1346.5 (the remainder is 1, so 2 is not a divisor of 2693)
2693 / 3 = 897.66666666667 (the remainder is 2, so 3 is not a divisor of 2693)
...
2693 / 2692 = 1.0003714710253 (the remainder is 1, so 2692 is not a divisor of 2693)
2693 / 2693 = 1 (the remainder is 0, so 2693 is a divisor of 2693)

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 2693 (i.e. 51.894122981316). 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 $\frac{N}{d} = D$ )

2693 / 1 = 2693 (the remainder is 0, so 1 and 2693 are divisors of 2693)
2693 / 2 = 1346.5 (the remainder is 1, so 2 is not a divisor of 2693)
2693 / 3 = 897.66666666667 (the remainder is 2, so 3 is not a divisor of 2693)
...
2693 / 50 = 53.86 (the remainder is 43, so 50 is not a divisor of 2693)
2693 / 51 = 52.803921568627 (the remainder is 41, so 51 is not a divisor of 2693)