What are the divisors of 2249?

1, 13, 173, 2249

There is a total of 4 positive divisors.
The sum of these divisors is 2436.
The arithmetic mean is 609.

4 odd divisors

1, 13, 173, 2249

How to compute the divisors of 2249?

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 2249 by each of the numbers from 1 to 2249 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)

2249 / 1 = 2249 (the remainder is 0, so 1 is a divisor of 2249)
2249 / 2 = 1124.5 (the remainder is 1, so 2 is not a divisor of 2249)
2249 / 3 = 749.66666666667 (the remainder is 2, so 3 is not a divisor of 2249)
...
2249 / 2248 = 1.0004448398577 (the remainder is 1, so 2248 is not a divisor of 2249)
2249 / 2249 = 1 (the remainder is 0, so 2249 is a divisor of 2249)

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 2249 (i.e. 47.423622805518). 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 $\frac{N}{d} = D$ )

2249 / 1 = 2249 (the remainder is 0, so 1 and 2249 are divisors of 2249)
2249 / 2 = 1124.5 (the remainder is 1, so 2 is not a divisor of 2249)
2249 / 3 = 749.66666666667 (the remainder is 2, so 3 is not a divisor of 2249)
...
2249 / 46 = 48.891304347826 (the remainder is 41, so 46 is not a divisor of 2249)
2249 / 47 = 47.851063829787 (the remainder is 40, so 47 is not a divisor of 2249)