What are the divisors of 4968?

1, 2, 3, 4, 6, 8, 9, 12, 18, 23, 24, 27, 36, 46, 54, 69, 72, 92, 108, 138, 184, 207, 216, 276, 414, 552, 621, 828, 1242, 1656, 2484, 4968

There is a total of 32 positive divisors.
The sum of these divisors is 14400.
The arithmetic mean is 450.

24 even divisors

2, 4, 6, 8, 12, 18, 24, 36, 46, 54, 72, 92, 108, 138, 184, 216, 276, 414, 552, 828, 1242, 1656, 2484, 4968

8 odd divisors

1, 3, 9, 23, 27, 69, 207, 621

How to compute the divisors of 4968?

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 4968 by each of the numbers from 1 to 4968 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)

4968 / 1 = 4968 (the remainder is 0, so 1 is a divisor of 4968)
4968 / 2 = 2484 (the remainder is 0, so 2 is a divisor of 4968)
4968 / 3 = 1656 (the remainder is 0, so 3 is a divisor of 4968)
...
4968 / 4967 = 1.0002013287699 (the remainder is 1, so 4967 is not a divisor of 4968)
4968 / 4968 = 1 (the remainder is 0, so 4968 is a divisor of 4968)

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 4968 (i.e. 70.484040746824). 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 $\frac{N}{d} = D$ )

4968 / 1 = 4968 (the remainder is 0, so 1 and 4968 are divisors of 4968)
4968 / 2 = 2484 (the remainder is 0, so 2 and 2484 are divisors of 4968)
4968 / 3 = 1656 (the remainder is 0, so 3 and 1656 are divisors of 4968)
...
4968 / 69 = 72 (the remainder is 0, so 69 and 72 are divisors of 4968)
4968 / 70 = 70.971428571429 (the remainder is 68, so 70 is not a divisor of 4968)