What are the divisors of 2521?

1, 2521

There is a total of 2 positive divisors.
The sum of these divisors is 2522.
The arithmetic mean is 1261.

2 odd divisors

1, 2521

How to compute the divisors of 2521?

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 2521 by each of the numbers from 1 to 2521 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)

2521 / 1 = 2521 (the remainder is 0, so 1 is a divisor of 2521)
2521 / 2 = 1260.5 (the remainder is 1, so 2 is not a divisor of 2521)
2521 / 3 = 840.33333333333 (the remainder is 1, so 3 is not a divisor of 2521)
...
2521 / 2520 = 1.0003968253968 (the remainder is 1, so 2520 is not a divisor of 2521)
2521 / 2521 = 1 (the remainder is 0, so 2521 is a divisor of 2521)

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 2521 (i.e. 50.209560842533). 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 $\frac{N}{d} = D$ )

2521 / 1 = 2521 (the remainder is 0, so 1 and 2521 are divisors of 2521)
2521 / 2 = 1260.5 (the remainder is 1, so 2 is not a divisor of 2521)
2521 / 3 = 840.33333333333 (the remainder is 1, so 3 is not a divisor of 2521)
...
2521 / 49 = 51.448979591837 (the remainder is 22, so 49 is not a divisor of 2521)
2521 / 50 = 50.42 (the remainder is 21, so 50 is not a divisor of 2521)