What are the divisors of 3454?

1, 2, 11, 22, 157, 314, 1727, 3454

There is a total of 8 positive divisors.
The sum of these divisors is 5688.
The arithmetic mean is 711.

4 even divisors

2, 22, 314, 3454

4 odd divisors

1, 11, 157, 1727

How to compute the divisors of 3454?

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 3454 by each of the numbers from 1 to 3454 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)

3454 / 1 = 3454 (the remainder is 0, so 1 is a divisor of 3454)
3454 / 2 = 1727 (the remainder is 0, so 2 is a divisor of 3454)
3454 / 3 = 1151.3333333333 (the remainder is 1, so 3 is not a divisor of 3454)
...
3454 / 3453 = 1.0002896032436 (the remainder is 1, so 3453 is not a divisor of 3454)
3454 / 3454 = 1 (the remainder is 0, so 3454 is a divisor of 3454)

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 3454 (i.e. 58.77074101966). 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 $\frac{N}{d} = D$ )

3454 / 1 = 3454 (the remainder is 0, so 1 and 3454 are divisors of 3454)
3454 / 2 = 1727 (the remainder is 0, so 2 and 1727 are divisors of 3454)
3454 / 3 = 1151.3333333333 (the remainder is 1, so 3 is not a divisor of 3454)
...
3454 / 57 = 60.59649122807 (the remainder is 34, so 57 is not a divisor of 3454)
3454 / 58 = 59.551724137931 (the remainder is 32, so 58 is not a divisor of 3454)