What are the divisors of 4514?

1, 2, 37, 61, 74, 122, 2257, 4514

There is a total of 8 positive divisors.
The sum of these divisors is 7068.
The arithmetic mean is 883.5.

4 even divisors

2, 74, 122, 4514

4 odd divisors

1, 37, 61, 2257

How to compute the divisors of 4514?

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 4514 by each of the numbers from 1 to 4514 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)

4514 / 1 = 4514 (the remainder is 0, so 1 is a divisor of 4514)
4514 / 2 = 2257 (the remainder is 0, so 2 is a divisor of 4514)
4514 / 3 = 1504.6666666667 (the remainder is 2, so 3 is not a divisor of 4514)
...
4514 / 4513 = 1.0002215820962 (the remainder is 1, so 4513 is not a divisor of 4514)
4514 / 4514 = 1 (the remainder is 0, so 4514 is a divisor of 4514)

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 4514 (i.e. 67.186308128963). 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 $\frac{N}{d} = D$ )

4514 / 1 = 4514 (the remainder is 0, so 1 and 4514 are divisors of 4514)
4514 / 2 = 2257 (the remainder is 0, so 2 and 2257 are divisors of 4514)
4514 / 3 = 1504.6666666667 (the remainder is 2, so 3 is not a divisor of 4514)
...
4514 / 66 = 68.393939393939 (the remainder is 26, so 66 is not a divisor of 4514)
4514 / 67 = 67.373134328358 (the remainder is 25, so 67 is not a divisor of 4514)