What are the divisors of 3467?

1, 3467

There is a total of 2 positive divisors.
The sum of these divisors is 3468.
The arithmetic mean is 1734.

2 odd divisors

1, 3467

How to compute the divisors of 3467?

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 3467 by each of the numbers from 1 to 3467 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)

3467 / 1 = 3467 (the remainder is 0, so 1 is a divisor of 3467)
3467 / 2 = 1733.5 (the remainder is 1, so 2 is not a divisor of 3467)
3467 / 3 = 1155.6666666667 (the remainder is 2, so 3 is not a divisor of 3467)
...
3467 / 3466 = 1.0002885170225 (the remainder is 1, so 3466 is not a divisor of 3467)
3467 / 3467 = 1 (the remainder is 0, so 3467 is a divisor of 3467)

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 3467 (i.e. 58.881236400062). 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 $\frac{N}{d} = D$ )

3467 / 1 = 3467 (the remainder is 0, so 1 and 3467 are divisors of 3467)
3467 / 2 = 1733.5 (the remainder is 1, so 2 is not a divisor of 3467)
3467 / 3 = 1155.6666666667 (the remainder is 2, so 3 is not a divisor of 3467)
...
3467 / 57 = 60.824561403509 (the remainder is 47, so 57 is not a divisor of 3467)
3467 / 58 = 59.775862068966 (the remainder is 45, so 58 is not a divisor of 3467)