What are the divisors of 2938?

1, 2, 13, 26, 113, 226, 1469, 2938

There is a total of 8 positive divisors.
The sum of these divisors is 4788.
The arithmetic mean is 598.5.

4 even divisors

2, 26, 226, 2938

4 odd divisors

1, 13, 113, 1469

How to compute the divisors of 2938?

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 2938 by each of the numbers from 1 to 2938 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)

2938 / 1 = 2938 (the remainder is 0, so 1 is a divisor of 2938)
2938 / 2 = 1469 (the remainder is 0, so 2 is a divisor of 2938)
2938 / 3 = 979.33333333333 (the remainder is 1, so 3 is not a divisor of 2938)
...
2938 / 2937 = 1.0003404834866 (the remainder is 1, so 2937 is not a divisor of 2938)
2938 / 2938 = 1 (the remainder is 0, so 2938 is a divisor of 2938)

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 2938 (i.e. 54.203320931471). 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 $\frac{N}{d} = D$ )

2938 / 1 = 2938 (the remainder is 0, so 1 and 2938 are divisors of 2938)
2938 / 2 = 1469 (the remainder is 0, so 2 and 1469 are divisors of 2938)
2938 / 3 = 979.33333333333 (the remainder is 1, so 3 is not a divisor of 2938)
...
2938 / 53 = 55.433962264151 (the remainder is 23, so 53 is not a divisor of 2938)
2938 / 54 = 54.407407407407 (the remainder is 22, so 54 is not a divisor of 2938)