What are the divisors of 4028?

1, 2, 4, 19, 38, 53, 76, 106, 212, 1007, 2014, 4028

There is a total of 12 positive divisors.
The sum of these divisors is 7560.
The arithmetic mean is 630.

8 even divisors

2, 4, 38, 76, 106, 212, 2014, 4028

4 odd divisors

1, 19, 53, 1007

How to compute the divisors of 4028?

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 4028 by each of the numbers from 1 to 4028 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)

4028 / 1 = 4028 (the remainder is 0, so 1 is a divisor of 4028)
4028 / 2 = 2014 (the remainder is 0, so 2 is a divisor of 4028)
4028 / 3 = 1342.6666666667 (the remainder is 2, so 3 is not a divisor of 4028)
...
4028 / 4027 = 1.0002483238143 (the remainder is 1, so 4027 is not a divisor of 4028)
4028 / 4028 = 1 (the remainder is 0, so 4028 is a divisor of 4028)

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 4028 (i.e. 63.46652661049). 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 $\frac{N}{d} = D$ )

4028 / 1 = 4028 (the remainder is 0, so 1 and 4028 are divisors of 4028)
4028 / 2 = 2014 (the remainder is 0, so 2 and 2014 are divisors of 4028)
4028 / 3 = 1342.6666666667 (the remainder is 2, so 3 is not a divisor of 4028)
...
4028 / 62 = 64.967741935484 (the remainder is 60, so 62 is not a divisor of 4028)
4028 / 63 = 63.936507936508 (the remainder is 59, so 63 is not a divisor of 4028)