What are the divisors of 2876?

1, 2, 4, 719, 1438, 2876

There is a total of 6 positive divisors.
The sum of these divisors is 5040.
The arithmetic mean is 840.

4 even divisors

2, 4, 1438, 2876

2 odd divisors

1, 719

How to compute the divisors of 2876?

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 2876 by each of the numbers from 1 to 2876 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)

2876 / 1 = 2876 (the remainder is 0, so 1 is a divisor of 2876)
2876 / 2 = 1438 (the remainder is 0, so 2 is a divisor of 2876)
2876 / 3 = 958.66666666667 (the remainder is 2, so 3 is not a divisor of 2876)
...
2876 / 2875 = 1.000347826087 (the remainder is 1, so 2875 is not a divisor of 2876)
2876 / 2876 = 1 (the remainder is 0, so 2876 is a divisor of 2876)

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 2876 (i.e. 53.628350711168). 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 $\frac{N}{d} = D$ )

2876 / 1 = 2876 (the remainder is 0, so 1 and 2876 are divisors of 2876)
2876 / 2 = 1438 (the remainder is 0, so 2 and 1438 are divisors of 2876)
2876 / 3 = 958.66666666667 (the remainder is 2, so 3 is not a divisor of 2876)
...
2876 / 52 = 55.307692307692 (the remainder is 16, so 52 is not a divisor of 2876)
2876 / 53 = 54.264150943396 (the remainder is 14, so 53 is not a divisor of 2876)