What are the divisors of 3437?

1, 7, 491, 3437

There is a total of 4 positive divisors.
The sum of these divisors is 3936.
The arithmetic mean is 984.

4 odd divisors

1, 7, 491, 3437

How to compute the divisors of 3437?

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 3437 by each of the numbers from 1 to 3437 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)

3437 / 1 = 3437 (the remainder is 0, so 1 is a divisor of 3437)
3437 / 2 = 1718.5 (the remainder is 1, so 2 is not a divisor of 3437)
3437 / 3 = 1145.6666666667 (the remainder is 2, so 3 is not a divisor of 3437)
...
3437 / 3436 = 1.0002910360885 (the remainder is 1, so 3436 is not a divisor of 3437)
3437 / 3437 = 1 (the remainder is 0, so 3437 is a divisor of 3437)

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 3437 (i.e. 58.625932828399). 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 $\frac{N}{d} = D$ )

3437 / 1 = 3437 (the remainder is 0, so 1 and 3437 are divisors of 3437)
3437 / 2 = 1718.5 (the remainder is 1, so 2 is not a divisor of 3437)
3437 / 3 = 1145.6666666667 (the remainder is 2, so 3 is not a divisor of 3437)
...
3437 / 57 = 60.298245614035 (the remainder is 17, so 57 is not a divisor of 3437)
3437 / 58 = 59.258620689655 (the remainder is 15, so 58 is not a divisor of 3437)