What are the divisors of 2674?

1, 2, 7, 14, 191, 382, 1337, 2674

There is a total of 8 positive divisors.
The sum of these divisors is 4608.
The arithmetic mean is 576.

4 even divisors

2, 14, 382, 2674

4 odd divisors

1, 7, 191, 1337

How to compute the divisors of 2674?

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 2674 by each of the numbers from 1 to 2674 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)

2674 / 1 = 2674 (the remainder is 0, so 1 is a divisor of 2674)
2674 / 2 = 1337 (the remainder is 0, so 2 is a divisor of 2674)
2674 / 3 = 891.33333333333 (the remainder is 1, so 3 is not a divisor of 2674)
...
2674 / 2673 = 1.0003741114852 (the remainder is 1, so 2673 is not a divisor of 2674)
2674 / 2674 = 1 (the remainder is 0, so 2674 is a divisor of 2674)

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 2674 (i.e. 51.710733895392). 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 $\frac{N}{d} = D$ )

2674 / 1 = 2674 (the remainder is 0, so 1 and 2674 are divisors of 2674)
2674 / 2 = 1337 (the remainder is 0, so 2 and 1337 are divisors of 2674)
2674 / 3 = 891.33333333333 (the remainder is 1, so 3 is not a divisor of 2674)
...
2674 / 50 = 53.48 (the remainder is 24, so 50 is not a divisor of 2674)
2674 / 51 = 52.43137254902 (the remainder is 22, so 51 is not a divisor of 2674)