What are the divisors of 4548?

1, 2, 3, 4, 6, 12, 379, 758, 1137, 1516, 2274, 4548

There is a total of 12 positive divisors.
The sum of these divisors is 10640.
The arithmetic mean is 886.66666666667.

8 even divisors

2, 4, 6, 12, 758, 1516, 2274, 4548

4 odd divisors

1, 3, 379, 1137

How to compute the divisors of 4548?

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 4548 by each of the numbers from 1 to 4548 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)

4548 / 1 = 4548 (the remainder is 0, so 1 is a divisor of 4548)
4548 / 2 = 2274 (the remainder is 0, so 2 is a divisor of 4548)
4548 / 3 = 1516 (the remainder is 0, so 3 is a divisor of 4548)
...
4548 / 4547 = 1.0002199252254 (the remainder is 1, so 4547 is not a divisor of 4548)
4548 / 4548 = 1 (the remainder is 0, so 4548 is a divisor of 4548)

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 4548 (i.e. 67.438861200349). 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 $\frac{N}{d} = D$ )

4548 / 1 = 4548 (the remainder is 0, so 1 and 4548 are divisors of 4548)
4548 / 2 = 2274 (the remainder is 0, so 2 and 2274 are divisors of 4548)
4548 / 3 = 1516 (the remainder is 0, so 3 and 1516 are divisors of 4548)
...
4548 / 66 = 68.909090909091 (the remainder is 60, so 66 is not a divisor of 4548)
4548 / 67 = 67.880597014925 (the remainder is 59, so 67 is not a divisor of 4548)