What are the divisors of 4884?

1, 2, 3, 4, 6, 11, 12, 22, 33, 37, 44, 66, 74, 111, 132, 148, 222, 407, 444, 814, 1221, 1628, 2442, 4884

There is a total of 24 positive divisors.
The sum of these divisors is 12768.
The arithmetic mean is 532.

16 even divisors

2, 4, 6, 12, 22, 44, 66, 74, 132, 148, 222, 444, 814, 1628, 2442, 4884

8 odd divisors

1, 3, 11, 33, 37, 111, 407, 1221

How to compute the divisors of 4884?

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 4884 by each of the numbers from 1 to 4884 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)

4884 / 1 = 4884 (the remainder is 0, so 1 is a divisor of 4884)
4884 / 2 = 2442 (the remainder is 0, so 2 is a divisor of 4884)
4884 / 3 = 1628 (the remainder is 0, so 3 is a divisor of 4884)
...
4884 / 4883 = 1.000204792136 (the remainder is 1, so 4883 is not a divisor of 4884)
4884 / 4884 = 1 (the remainder is 0, so 4884 is a divisor of 4884)

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 4884 (i.e. 69.885620838625). 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 $\frac{N}{d} = D$ )

4884 / 1 = 4884 (the remainder is 0, so 1 and 4884 are divisors of 4884)
4884 / 2 = 2442 (the remainder is 0, so 2 and 2442 are divisors of 4884)
4884 / 3 = 1628 (the remainder is 0, so 3 and 1628 are divisors of 4884)
...
4884 / 68 = 71.823529411765 (the remainder is 56, so 68 is not a divisor of 4884)
4884 / 69 = 70.782608695652 (the remainder is 54, so 69 is not a divisor of 4884)