What are the divisors of 3400?

1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, 3400

There is a total of 24 positive divisors.
The sum of these divisors is 8370.
The arithmetic mean is 348.75.

18 even divisors

2, 4, 8, 10, 20, 34, 40, 50, 68, 100, 136, 170, 200, 340, 680, 850, 1700, 3400

6 odd divisors

1, 5, 17, 25, 85, 425

How to compute the divisors of 3400?

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 3400 by each of the numbers from 1 to 3400 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)

3400 / 1 = 3400 (the remainder is 0, so 1 is a divisor of 3400)
3400 / 2 = 1700 (the remainder is 0, so 2 is a divisor of 3400)
3400 / 3 = 1133.3333333333 (the remainder is 1, so 3 is not a divisor of 3400)
...
3400 / 3399 = 1.0002942041777 (the remainder is 1, so 3399 is not a divisor of 3400)
3400 / 3400 = 1 (the remainder is 0, so 3400 is a divisor of 3400)

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 3400 (i.e. 58.309518948453). 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 $\frac{N}{d} = D$ )

3400 / 1 = 3400 (the remainder is 0, so 1 and 3400 are divisors of 3400)
3400 / 2 = 1700 (the remainder is 0, so 2 and 1700 are divisors of 3400)
3400 / 3 = 1133.3333333333 (the remainder is 1, so 3 is not a divisor of 3400)
...
3400 / 57 = 59.649122807018 (the remainder is 37, so 57 is not a divisor of 3400)
3400 / 58 = 58.620689655172 (the remainder is 36, so 58 is not a divisor of 3400)