What are the divisors of 2449?

1, 31, 79, 2449

There is a total of 4 positive divisors.
The sum of these divisors is 2560.
The arithmetic mean is 640.

4 odd divisors

1, 31, 79, 2449

How to compute the divisors of 2449?

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 2449 by each of the numbers from 1 to 2449 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)

2449 / 1 = 2449 (the remainder is 0, so 1 is a divisor of 2449)
2449 / 2 = 1224.5 (the remainder is 1, so 2 is not a divisor of 2449)
2449 / 3 = 816.33333333333 (the remainder is 1, so 3 is not a divisor of 2449)
...
2449 / 2448 = 1.000408496732 (the remainder is 1, so 2448 is not a divisor of 2449)
2449 / 2449 = 1 (the remainder is 0, so 2449 is a divisor of 2449)

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 2449 (i.e. 49.487372126634). 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 $\frac{N}{d} = D$ )

2449 / 1 = 2449 (the remainder is 0, so 1 and 2449 are divisors of 2449)
2449 / 2 = 1224.5 (the remainder is 1, so 2 is not a divisor of 2449)
2449 / 3 = 816.33333333333 (the remainder is 1, so 3 is not a divisor of 2449)
...
2449 / 48 = 51.020833333333 (the remainder is 1, so 48 is not a divisor of 2449)
2449 / 49 = 49.979591836735 (the remainder is 48, so 49 is not a divisor of 2449)