What are the divisors of 3431?

1, 47, 73, 3431

There is a total of 4 positive divisors.
The sum of these divisors is 3552.
The arithmetic mean is 888.

4 odd divisors

1, 47, 73, 3431

How to compute the divisors of 3431?

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 3431 by each of the numbers from 1 to 3431 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)

3431 / 1 = 3431 (the remainder is 0, so 1 is a divisor of 3431)
3431 / 2 = 1715.5 (the remainder is 1, so 2 is not a divisor of 3431)
3431 / 3 = 1143.6666666667 (the remainder is 2, so 3 is not a divisor of 3431)
...
3431 / 3430 = 1.0002915451895 (the remainder is 1, so 3430 is not a divisor of 3431)
3431 / 3431 = 1 (the remainder is 0, so 3431 is a divisor of 3431)

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 3431 (i.e. 58.57473858243). 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 $\frac{N}{d} = D$ )

3431 / 1 = 3431 (the remainder is 0, so 1 and 3431 are divisors of 3431)
3431 / 2 = 1715.5 (the remainder is 1, so 2 is not a divisor of 3431)
3431 / 3 = 1143.6666666667 (the remainder is 2, so 3 is not a divisor of 3431)
...
3431 / 57 = 60.19298245614 (the remainder is 11, so 57 is not a divisor of 3431)
3431 / 58 = 59.155172413793 (the remainder is 9, so 58 is not a divisor of 3431)