What are the divisors of 5514?

1, 2, 3, 6, 919, 1838, 2757, 5514

There is a total of 8 positive divisors.
The sum of these divisors is 11040.
The arithmetic mean is 1380.

4 even divisors

2, 6, 1838, 5514

4 odd divisors

1, 3, 919, 2757

How to compute the divisors of 5514?

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 5514 by each of the numbers from 1 to 5514 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)

5514 / 1 = 5514 (the remainder is 0, so 1 is a divisor of 5514)
5514 / 2 = 2757 (the remainder is 0, so 2 is a divisor of 5514)
5514 / 3 = 1838 (the remainder is 0, so 3 is a divisor of 5514)
...
5514 / 5513 = 1.0001813894431 (the remainder is 1, so 5513 is not a divisor of 5514)
5514 / 5514 = 1 (the remainder is 0, so 5514 is a divisor of 5514)

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 5514 (i.e. 74.256312862948). 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 $\frac{N}{d} = D$ )

5514 / 1 = 5514 (the remainder is 0, so 1 and 5514 are divisors of 5514)
5514 / 2 = 2757 (the remainder is 0, so 2 and 2757 are divisors of 5514)
5514 / 3 = 1838 (the remainder is 0, so 3 and 1838 are divisors of 5514)
...
5514 / 73 = 75.534246575342 (the remainder is 39, so 73 is not a divisor of 5514)
5514 / 74 = 74.513513513514 (the remainder is 38, so 74 is not a divisor of 5514)