What are the divisors of 2545?

1, 5, 509, 2545

There is a total of 4 positive divisors.
The sum of these divisors is 3060.
The arithmetic mean is 765.

4 odd divisors

1, 5, 509, 2545

How to compute the divisors of 2545?

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 2545 by each of the numbers from 1 to 2545 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)

2545 / 1 = 2545 (the remainder is 0, so 1 is a divisor of 2545)
2545 / 2 = 1272.5 (the remainder is 1, so 2 is not a divisor of 2545)
2545 / 3 = 848.33333333333 (the remainder is 1, so 3 is not a divisor of 2545)
...
2545 / 2544 = 1.000393081761 (the remainder is 1, so 2544 is not a divisor of 2545)
2545 / 2545 = 1 (the remainder is 0, so 2545 is a divisor of 2545)

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 2545 (i.e. 50.447993022518). 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 $\frac{N}{d} = D$ )

2545 / 1 = 2545 (the remainder is 0, so 1 and 2545 are divisors of 2545)
2545 / 2 = 1272.5 (the remainder is 1, so 2 is not a divisor of 2545)
2545 / 3 = 848.33333333333 (the remainder is 1, so 3 is not a divisor of 2545)
...
2545 / 49 = 51.938775510204 (the remainder is 46, so 49 is not a divisor of 2545)
2545 / 50 = 50.9 (the remainder is 45, so 50 is not a divisor of 2545)