What are the divisors of 2338?

1, 2, 7, 14, 167, 334, 1169, 2338

There is a total of 8 positive divisors.
The sum of these divisors is 4032.
The arithmetic mean is 504.

4 even divisors

2, 14, 334, 2338

4 odd divisors

1, 7, 167, 1169

How to compute the divisors of 2338?

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 2338 by each of the numbers from 1 to 2338 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)

2338 / 1 = 2338 (the remainder is 0, so 1 is a divisor of 2338)
2338 / 2 = 1169 (the remainder is 0, so 2 is a divisor of 2338)
2338 / 3 = 779.33333333333 (the remainder is 1, so 3 is not a divisor of 2338)
...
2338 / 2337 = 1.0004278990158 (the remainder is 1, so 2337 is not a divisor of 2338)
2338 / 2338 = 1 (the remainder is 0, so 2338 is a divisor of 2338)

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 2338 (i.e. 48.352869614946). 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 $\frac{N}{d} = D$ )

2338 / 1 = 2338 (the remainder is 0, so 1 and 2338 are divisors of 2338)
2338 / 2 = 1169 (the remainder is 0, so 2 and 1169 are divisors of 2338)
2338 / 3 = 779.33333333333 (the remainder is 1, so 3 is not a divisor of 2338)
...
2338 / 47 = 49.744680851064 (the remainder is 35, so 47 is not a divisor of 2338)
2338 / 48 = 48.708333333333 (the remainder is 34, so 48 is not a divisor of 2338)