What are the divisors of 3452?

1, 2, 4, 863, 1726, 3452

There is a total of 6 positive divisors.
The sum of these divisors is 6048.
The arithmetic mean is 1008.

4 even divisors

2, 4, 1726, 3452

2 odd divisors

1, 863

How to compute the divisors of 3452?

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 3452 by each of the numbers from 1 to 3452 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)

3452 / 1 = 3452 (the remainder is 0, so 1 is a divisor of 3452)
3452 / 2 = 1726 (the remainder is 0, so 2 is a divisor of 3452)
3452 / 3 = 1150.6666666667 (the remainder is 2, so 3 is not a divisor of 3452)
...
3452 / 3451 = 1.0002897710808 (the remainder is 1, so 3451 is not a divisor of 3452)
3452 / 3452 = 1 (the remainder is 0, so 3452 is a divisor of 3452)

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 3452 (i.e. 58.753723286274). 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 $\frac{N}{d} = D$ )

3452 / 1 = 3452 (the remainder is 0, so 1 and 3452 are divisors of 3452)
3452 / 2 = 1726 (the remainder is 0, so 2 and 1726 are divisors of 3452)
3452 / 3 = 1150.6666666667 (the remainder is 2, so 3 is not a divisor of 3452)
...
3452 / 57 = 60.561403508772 (the remainder is 32, so 57 is not a divisor of 3452)
3452 / 58 = 59.51724137931 (the remainder is 30, so 58 is not a divisor of 3452)