What are the divisors of 2237?

1, 2237

There is a total of 2 positive divisors.
The sum of these divisors is 2238.
The arithmetic mean is 1119.

2 odd divisors

1, 2237

How to compute the divisors of 2237?

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 2237 by each of the numbers from 1 to 2237 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)

2237 / 1 = 2237 (the remainder is 0, so 1 is a divisor of 2237)
2237 / 2 = 1118.5 (the remainder is 1, so 2 is not a divisor of 2237)
2237 / 3 = 745.66666666667 (the remainder is 2, so 3 is not a divisor of 2237)
...
2237 / 2236 = 1.0004472271914 (the remainder is 1, so 2236 is not a divisor of 2237)
2237 / 2237 = 1 (the remainder is 0, so 2237 is a divisor of 2237)

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 2237 (i.e. 47.296934361542). 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 $\frac{N}{d} = D$ )

2237 / 1 = 2237 (the remainder is 0, so 1 and 2237 are divisors of 2237)
2237 / 2 = 1118.5 (the remainder is 1, so 2 is not a divisor of 2237)
2237 / 3 = 745.66666666667 (the remainder is 2, so 3 is not a divisor of 2237)
...
2237 / 46 = 48.630434782609 (the remainder is 29, so 46 is not a divisor of 2237)
2237 / 47 = 47.595744680851 (the remainder is 28, so 47 is not a divisor of 2237)