What are the divisors of 2671?

1, 2671

There is a total of 2 positive divisors.
The sum of these divisors is 2672.
The arithmetic mean is 1336.

2 odd divisors

1, 2671

How to compute the divisors of 2671?

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 2671 by each of the numbers from 1 to 2671 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)

2671 / 1 = 2671 (the remainder is 0, so 1 is a divisor of 2671)
2671 / 2 = 1335.5 (the remainder is 1, so 2 is not a divisor of 2671)
2671 / 3 = 890.33333333333 (the remainder is 1, so 3 is not a divisor of 2671)
...
2671 / 2670 = 1.0003745318352 (the remainder is 1, so 2670 is not a divisor of 2671)
2671 / 2671 = 1 (the remainder is 0, so 2671 is a divisor of 2671)

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 2671 (i.e. 51.68171823769). 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 $\frac{N}{d} = D$ )

2671 / 1 = 2671 (the remainder is 0, so 1 and 2671 are divisors of 2671)
2671 / 2 = 1335.5 (the remainder is 1, so 2 is not a divisor of 2671)
2671 / 3 = 890.33333333333 (the remainder is 1, so 3 is not a divisor of 2671)
...
2671 / 50 = 53.42 (the remainder is 21, so 50 is not a divisor of 2671)
2671 / 51 = 52.372549019608 (the remainder is 19, so 51 is not a divisor of 2671)