What are the divisors of 4280?

1, 2, 4, 5, 8, 10, 20, 40, 107, 214, 428, 535, 856, 1070, 2140, 4280

There is a total of 16 positive divisors.
The sum of these divisors is 9720.
The arithmetic mean is 607.5.

12 even divisors

2, 4, 8, 10, 20, 40, 214, 428, 856, 1070, 2140, 4280

4 odd divisors

1, 5, 107, 535

How to compute the divisors of 4280?

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 4280 by each of the numbers from 1 to 4280 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)

4280 / 1 = 4280 (the remainder is 0, so 1 is a divisor of 4280)
4280 / 2 = 2140 (the remainder is 0, so 2 is a divisor of 4280)
4280 / 3 = 1426.6666666667 (the remainder is 2, so 3 is not a divisor of 4280)
...
4280 / 4279 = 1.0002336994625 (the remainder is 1, so 4279 is not a divisor of 4280)
4280 / 4280 = 1 (the remainder is 0, so 4280 is a divisor of 4280)

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 4280 (i.e. 65.421708935184). 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 $\frac{N}{d} = D$ )

4280 / 1 = 4280 (the remainder is 0, so 1 and 4280 are divisors of 4280)
4280 / 2 = 2140 (the remainder is 0, so 2 and 2140 are divisors of 4280)
4280 / 3 = 1426.6666666667 (the remainder is 2, so 3 is not a divisor of 4280)
...
4280 / 64 = 66.875 (the remainder is 56, so 64 is not a divisor of 4280)
4280 / 65 = 65.846153846154 (the remainder is 55, so 65 is not a divisor of 4280)