What are the divisors of 2913?

1, 3, 971, 2913

There is a total of 4 positive divisors.
The sum of these divisors is 3888.
The arithmetic mean is 972.

4 odd divisors

1, 3, 971, 2913

How to compute the divisors of 2913?

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 2913 by each of the numbers from 1 to 2913 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)

2913 / 1 = 2913 (the remainder is 0, so 1 is a divisor of 2913)
2913 / 2 = 1456.5 (the remainder is 1, so 2 is not a divisor of 2913)
2913 / 3 = 971 (the remainder is 0, so 3 is a divisor of 2913)
...
2913 / 2912 = 1.0003434065934 (the remainder is 1, so 2912 is not a divisor of 2913)
2913 / 2913 = 1 (the remainder is 0, so 2913 is a divisor of 2913)

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 2913 (i.e. 53.972215074055). 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 $\frac{N}{d} = D$ )

2913 / 1 = 2913 (the remainder is 0, so 1 and 2913 are divisors of 2913)
2913 / 2 = 1456.5 (the remainder is 1, so 2 is not a divisor of 2913)
2913 / 3 = 971 (the remainder is 0, so 3 and 971 are divisors of 2913)
...
2913 / 52 = 56.019230769231 (the remainder is 1, so 52 is not a divisor of 2913)
2913 / 53 = 54.962264150943 (the remainder is 51, so 53 is not a divisor of 2913)