What are the divisors of 3427?

1, 23, 149, 3427

There is a total of 4 positive divisors.
The sum of these divisors is 3600.
The arithmetic mean is 900.

4 odd divisors

1, 23, 149, 3427

How to compute the divisors of 3427?

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 3427 by each of the numbers from 1 to 3427 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)

3427 / 1 = 3427 (the remainder is 0, so 1 is a divisor of 3427)
3427 / 2 = 1713.5 (the remainder is 1, so 2 is not a divisor of 3427)
3427 / 3 = 1142.3333333333 (the remainder is 1, so 3 is not a divisor of 3427)
...
3427 / 3426 = 1.0002918855809 (the remainder is 1, so 3426 is not a divisor of 3427)
3427 / 3427 = 1 (the remainder is 0, so 3427 is a divisor of 3427)

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 3427 (i.e. 58.540584213006). 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 $\frac{N}{d} = D$ )

3427 / 1 = 3427 (the remainder is 0, so 1 and 3427 are divisors of 3427)
3427 / 2 = 1713.5 (the remainder is 1, so 2 is not a divisor of 3427)
3427 / 3 = 1142.3333333333 (the remainder is 1, so 3 is not a divisor of 3427)
...
3427 / 57 = 60.122807017544 (the remainder is 7, so 57 is not a divisor of 3427)
3427 / 58 = 59.086206896552 (the remainder is 5, so 58 is not a divisor of 3427)