What are the divisors of 4248?

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 59, 72, 118, 177, 236, 354, 472, 531, 708, 1062, 1416, 2124, 4248

There is a total of 24 positive divisors.
The sum of these divisors is 11700.
The arithmetic mean is 487.5.

18 even divisors

2, 4, 6, 8, 12, 18, 24, 36, 72, 118, 236, 354, 472, 708, 1062, 1416, 2124, 4248

6 odd divisors

1, 3, 9, 59, 177, 531

How to compute the divisors of 4248?

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 4248 by each of the numbers from 1 to 4248 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)

4248 / 1 = 4248 (the remainder is 0, so 1 is a divisor of 4248)
4248 / 2 = 2124 (the remainder is 0, so 2 is a divisor of 4248)
4248 / 3 = 1416 (the remainder is 0, so 3 is a divisor of 4248)
...
4248 / 4247 = 1.0002354603249 (the remainder is 1, so 4247 is not a divisor of 4248)
4248 / 4248 = 1 (the remainder is 0, so 4248 is a divisor of 4248)

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 4248 (i.e. 65.176682947201). 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 $\frac{N}{d} = D$ )

4248 / 1 = 4248 (the remainder is 0, so 1 and 4248 are divisors of 4248)
4248 / 2 = 2124 (the remainder is 0, so 2 and 2124 are divisors of 4248)
4248 / 3 = 1416 (the remainder is 0, so 3 and 1416 are divisors of 4248)
...
4248 / 64 = 66.375 (the remainder is 24, so 64 is not a divisor of 4248)
4248 / 65 = 65.353846153846 (the remainder is 23, so 65 is not a divisor of 4248)