What are the divisors of 3460?

1, 2, 4, 5, 10, 20, 173, 346, 692, 865, 1730, 3460

There is a total of 12 positive divisors.
The sum of these divisors is 7308.
The arithmetic mean is 609.

8 even divisors

2, 4, 10, 20, 346, 692, 1730, 3460

4 odd divisors

1, 5, 173, 865

How to compute the divisors of 3460?

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 3460 by each of the numbers from 1 to 3460 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)

3460 / 1 = 3460 (the remainder is 0, so 1 is a divisor of 3460)
3460 / 2 = 1730 (the remainder is 0, so 2 is a divisor of 3460)
3460 / 3 = 1153.3333333333 (the remainder is 1, so 3 is not a divisor of 3460)
...
3460 / 3459 = 1.0002891008962 (the remainder is 1, so 3459 is not a divisor of 3460)
3460 / 3460 = 1 (the remainder is 0, so 3460 is a divisor of 3460)

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 3460 (i.e. 58.821764679411). 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 $\frac{N}{d} = D$ )

3460 / 1 = 3460 (the remainder is 0, so 1 and 3460 are divisors of 3460)
3460 / 2 = 1730 (the remainder is 0, so 2 and 1730 are divisors of 3460)
3460 / 3 = 1153.3333333333 (the remainder is 1, so 3 is not a divisor of 3460)
...
3460 / 57 = 60.701754385965 (the remainder is 40, so 57 is not a divisor of 3460)
3460 / 58 = 59.655172413793 (the remainder is 38, so 58 is not a divisor of 3460)