What are the divisors of 2879?

1, 2879

There is a total of 2 positive divisors.
The sum of these divisors is 2880.
The arithmetic mean is 1440.

2 odd divisors

1, 2879

How to compute the divisors of 2879?

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 2879 by each of the numbers from 1 to 2879 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)

2879 / 1 = 2879 (the remainder is 0, so 1 is a divisor of 2879)
2879 / 2 = 1439.5 (the remainder is 1, so 2 is not a divisor of 2879)
2879 / 3 = 959.66666666667 (the remainder is 2, so 3 is not a divisor of 2879)
...
2879 / 2878 = 1.0003474635163 (the remainder is 1, so 2878 is not a divisor of 2879)
2879 / 2879 = 1 (the remainder is 0, so 2879 is a divisor of 2879)

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 2879 (i.e. 53.656313701185). 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 $\frac{N}{d} = D$ )

2879 / 1 = 2879 (the remainder is 0, so 1 and 2879 are divisors of 2879)
2879 / 2 = 1439.5 (the remainder is 1, so 2 is not a divisor of 2879)
2879 / 3 = 959.66666666667 (the remainder is 2, so 3 is not a divisor of 2879)
...
2879 / 52 = 55.365384615385 (the remainder is 19, so 52 is not a divisor of 2879)
2879 / 53 = 54.320754716981 (the remainder is 17, so 53 is not a divisor of 2879)