What are the divisors of 3463?

1, 3463

There is a total of 2 positive divisors.
The sum of these divisors is 3464.
The arithmetic mean is 1732.

2 odd divisors

1, 3463

How to compute the divisors of 3463?

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 3463 by each of the numbers from 1 to 3463 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)

3463 / 1 = 3463 (the remainder is 0, so 1 is a divisor of 3463)
3463 / 2 = 1731.5 (the remainder is 1, so 2 is not a divisor of 3463)
3463 / 3 = 1154.3333333333 (the remainder is 1, so 3 is not a divisor of 3463)
...
3463 / 3462 = 1.0002888503755 (the remainder is 1, so 3462 is not a divisor of 3463)
3463 / 3463 = 1 (the remainder is 0, so 3463 is a divisor of 3463)

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 3463 (i.e. 58.847259919218). 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 $\frac{N}{d} = D$ )

3463 / 1 = 3463 (the remainder is 0, so 1 and 3463 are divisors of 3463)
3463 / 2 = 1731.5 (the remainder is 1, so 2 is not a divisor of 3463)
3463 / 3 = 1154.3333333333 (the remainder is 1, so 3 is not a divisor of 3463)
...
3463 / 57 = 60.754385964912 (the remainder is 43, so 57 is not a divisor of 3463)
3463 / 58 = 59.706896551724 (the remainder is 41, so 58 is not a divisor of 3463)