What are the divisors of 3445?

1, 5, 13, 53, 65, 265, 689, 3445

There is a total of 8 positive divisors.
The sum of these divisors is 4536.
The arithmetic mean is 567.

8 odd divisors

1, 5, 13, 53, 65, 265, 689, 3445

How to compute the divisors of 3445?

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 3445 by each of the numbers from 1 to 3445 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)

3445 / 1 = 3445 (the remainder is 0, so 1 is a divisor of 3445)
3445 / 2 = 1722.5 (the remainder is 1, so 2 is not a divisor of 3445)
3445 / 3 = 1148.3333333333 (the remainder is 1, so 3 is not a divisor of 3445)
...
3445 / 3444 = 1.0002903600465 (the remainder is 1, so 3444 is not a divisor of 3445)
3445 / 3445 = 1 (the remainder is 0, so 3445 is a divisor of 3445)

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 3445 (i.e. 58.694122363317). 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 $\frac{N}{d} = D$ )

3445 / 1 = 3445 (the remainder is 0, so 1 and 3445 are divisors of 3445)
3445 / 2 = 1722.5 (the remainder is 1, so 2 is not a divisor of 3445)
3445 / 3 = 1148.3333333333 (the remainder is 1, so 3 is not a divisor of 3445)
...
3445 / 57 = 60.438596491228 (the remainder is 25, so 57 is not a divisor of 3445)
3445 / 58 = 59.396551724138 (the remainder is 23, so 58 is not a divisor of 3445)