What are the divisors of 2918?

1, 2, 1459, 2918

There is a total of 4 positive divisors.
The sum of these divisors is 4380.
The arithmetic mean is 1095.

2 even divisors

2, 2918

2 odd divisors

1, 1459

How to compute the divisors of 2918?

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 2918 by each of the numbers from 1 to 2918 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)

2918 / 1 = 2918 (the remainder is 0, so 1 is a divisor of 2918)
2918 / 2 = 1459 (the remainder is 0, so 2 is a divisor of 2918)
2918 / 3 = 972.66666666667 (the remainder is 2, so 3 is not a divisor of 2918)
...
2918 / 2917 = 1.0003428179637 (the remainder is 1, so 2917 is not a divisor of 2918)
2918 / 2918 = 1 (the remainder is 0, so 2918 is a divisor of 2918)

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 2918 (i.e. 54.018515344278). 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 $\frac{N}{d} = D$ )

2918 / 1 = 2918 (the remainder is 0, so 1 and 2918 are divisors of 2918)
2918 / 2 = 1459 (the remainder is 0, so 2 and 1459 are divisors of 2918)
2918 / 3 = 972.66666666667 (the remainder is 2, so 3 is not a divisor of 2918)
...
2918 / 53 = 55.056603773585 (the remainder is 3, so 53 is not a divisor of 2918)
2918 / 54 = 54.037037037037 (the remainder is 2, so 54 is not a divisor of 2918)