What are the divisors of 2437?

1, 2437

There is a total of 2 positive divisors.
The sum of these divisors is 2438.
The arithmetic mean is 1219.

2 odd divisors

1, 2437

How to compute the divisors of 2437?

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 2437 by each of the numbers from 1 to 2437 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)

2437 / 1 = 2437 (the remainder is 0, so 1 is a divisor of 2437)
2437 / 2 = 1218.5 (the remainder is 1, so 2 is not a divisor of 2437)
2437 / 3 = 812.33333333333 (the remainder is 1, so 3 is not a divisor of 2437)
...
2437 / 2436 = 1.0004105090312 (the remainder is 1, so 2436 is not a divisor of 2437)
2437 / 2437 = 1 (the remainder is 0, so 2437 is a divisor of 2437)

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 2437 (i.e. 49.36598018879). 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 $\frac{N}{d} = D$ )

2437 / 1 = 2437 (the remainder is 0, so 1 and 2437 are divisors of 2437)
2437 / 2 = 1218.5 (the remainder is 1, so 2 is not a divisor of 2437)
2437 / 3 = 812.33333333333 (the remainder is 1, so 3 is not a divisor of 2437)
...
2437 / 48 = 50.770833333333 (the remainder is 37, so 48 is not a divisor of 2437)
2437 / 49 = 49.734693877551 (the remainder is 36, so 49 is not a divisor of 2437)