What are the divisors of 4240?

1, 2, 4, 5, 8, 10, 16, 20, 40, 53, 80, 106, 212, 265, 424, 530, 848, 1060, 2120, 4240

There is a total of 20 positive divisors.
The sum of these divisors is 10044.
The arithmetic mean is 502.2.

16 even divisors

2, 4, 8, 10, 16, 20, 40, 80, 106, 212, 424, 530, 848, 1060, 2120, 4240

4 odd divisors

1, 5, 53, 265

How to compute the divisors of 4240?

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 4240 by each of the numbers from 1 to 4240 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)

4240 / 1 = 4240 (the remainder is 0, so 1 is a divisor of 4240)
4240 / 2 = 2120 (the remainder is 0, so 2 is a divisor of 4240)
4240 / 3 = 1413.3333333333 (the remainder is 1, so 3 is not a divisor of 4240)
...
4240 / 4239 = 1.0002359046945 (the remainder is 1, so 4239 is not a divisor of 4240)
4240 / 4240 = 1 (the remainder is 0, so 4240 is a divisor of 4240)

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 4240 (i.e. 65.115282384399). 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 $\frac{N}{d} = D$ )

4240 / 1 = 4240 (the remainder is 0, so 1 and 4240 are divisors of 4240)
4240 / 2 = 2120 (the remainder is 0, so 2 and 2120 are divisors of 4240)
4240 / 3 = 1413.3333333333 (the remainder is 1, so 3 is not a divisor of 4240)
...
4240 / 64 = 66.25 (the remainder is 16, so 64 is not a divisor of 4240)
4240 / 65 = 65.230769230769 (the remainder is 15, so 65 is not a divisor of 4240)