What are the divisors of 3428?

1, 2, 4, 857, 1714, 3428

There is a total of 6 positive divisors.
The sum of these divisors is 6006.
The arithmetic mean is 1001.

4 even divisors

2, 4, 1714, 3428

2 odd divisors

1, 857

How to compute the divisors of 3428?

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 3428 by each of the numbers from 1 to 3428 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)

3428 / 1 = 3428 (the remainder is 0, so 1 is a divisor of 3428)
3428 / 2 = 1714 (the remainder is 0, so 2 is a divisor of 3428)
3428 / 3 = 1142.6666666667 (the remainder is 2, so 3 is not a divisor of 3428)
...
3428 / 3427 = 1.0002918004085 (the remainder is 1, so 3427 is not a divisor of 3428)
3428 / 3428 = 1 (the remainder is 0, so 3428 is a divisor of 3428)

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 3428 (i.e. 58.549124673218). 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 $\frac{N}{d} = D$ )

3428 / 1 = 3428 (the remainder is 0, so 1 and 3428 are divisors of 3428)
3428 / 2 = 1714 (the remainder is 0, so 2 and 1714 are divisors of 3428)
3428 / 3 = 1142.6666666667 (the remainder is 2, so 3 is not a divisor of 3428)
...
3428 / 57 = 60.140350877193 (the remainder is 8, so 57 is not a divisor of 3428)
3428 / 58 = 59.103448275862 (the remainder is 6, so 58 is not a divisor of 3428)