What are the divisors of 2514?

1, 2, 3, 6, 419, 838, 1257, 2514

There is a total of 8 positive divisors.
The sum of these divisors is 5040.
The arithmetic mean is 630.

4 even divisors

2, 6, 838, 2514

4 odd divisors

1, 3, 419, 1257

How to compute the divisors of 2514?

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 2514 by each of the numbers from 1 to 2514 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)

2514 / 1 = 2514 (the remainder is 0, so 1 is a divisor of 2514)
2514 / 2 = 1257 (the remainder is 0, so 2 is a divisor of 2514)
2514 / 3 = 838 (the remainder is 0, so 3 is a divisor of 2514)
...
2514 / 2513 = 1.00039793076 (the remainder is 1, so 2513 is not a divisor of 2514)
2514 / 2514 = 1 (the remainder is 0, so 2514 is a divisor of 2514)

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 2514 (i.e. 50.139804546887). 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 $\frac{N}{d} = D$ )

2514 / 1 = 2514 (the remainder is 0, so 1 and 2514 are divisors of 2514)
2514 / 2 = 1257 (the remainder is 0, so 2 and 1257 are divisors of 2514)
2514 / 3 = 838 (the remainder is 0, so 3 and 838 are divisors of 2514)
...
2514 / 49 = 51.30612244898 (the remainder is 15, so 49 is not a divisor of 2514)
2514 / 50 = 50.28 (the remainder is 14, so 50 is not a divisor of 2514)