What are the divisors of 4284?

1, 2, 3, 4, 6, 7, 9, 12, 14, 17, 18, 21, 28, 34, 36, 42, 51, 63, 68, 84, 102, 119, 126, 153, 204, 238, 252, 306, 357, 476, 612, 714, 1071, 1428, 2142, 4284

There is a total of 36 positive divisors.
The sum of these divisors is 13104.
The arithmetic mean is 364.

24 even divisors

2, 4, 6, 12, 14, 18, 28, 34, 36, 42, 68, 84, 102, 126, 204, 238, 252, 306, 476, 612, 714, 1428, 2142, 4284

12 odd divisors

1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357, 1071

How to compute the divisors of 4284?

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 4284 by each of the numbers from 1 to 4284 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)

4284 / 1 = 4284 (the remainder is 0, so 1 is a divisor of 4284)
4284 / 2 = 2142 (the remainder is 0, so 2 is a divisor of 4284)
4284 / 3 = 1428 (the remainder is 0, so 3 is a divisor of 4284)
...
4284 / 4283 = 1.0002334812048 (the remainder is 1, so 4283 is not a divisor of 4284)
4284 / 4284 = 1 (the remainder is 0, so 4284 is a divisor of 4284)

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 4284 (i.e. 65.452272687814). 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 $\frac{N}{d} = D$ )

4284 / 1 = 4284 (the remainder is 0, so 1 and 4284 are divisors of 4284)
4284 / 2 = 2142 (the remainder is 0, so 2 and 2142 are divisors of 4284)
4284 / 3 = 1428 (the remainder is 0, so 3 and 1428 are divisors of 4284)
...
4284 / 64 = 66.9375 (the remainder is 60, so 64 is not a divisor of 4284)
4284 / 65 = 65.907692307692 (the remainder is 59, so 65 is not a divisor of 4284)