What are the divisors of 3354?

1, 2, 3, 6, 13, 26, 39, 43, 78, 86, 129, 258, 559, 1118, 1677, 3354

There is a total of 16 positive divisors.
The sum of these divisors is 7392.
The arithmetic mean is 462.

8 even divisors

2, 6, 26, 78, 86, 258, 1118, 3354

8 odd divisors

1, 3, 13, 39, 43, 129, 559, 1677

How to compute the divisors of 3354?

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 3354 by each of the numbers from 1 to 3354 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)

3354 / 1 = 3354 (the remainder is 0, so 1 is a divisor of 3354)
3354 / 2 = 1677 (the remainder is 0, so 2 is a divisor of 3354)
3354 / 3 = 1118 (the remainder is 0, so 3 is a divisor of 3354)
...
3354 / 3353 = 1.0002982403817 (the remainder is 1, so 3353 is not a divisor of 3354)
3354 / 3354 = 1 (the remainder is 0, so 3354 is a divisor of 3354)

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 3354 (i.e. 57.913728942281). 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 $\frac{N}{d} = D$ )

3354 / 1 = 3354 (the remainder is 0, so 1 and 3354 are divisors of 3354)
3354 / 2 = 1677 (the remainder is 0, so 2 and 1677 are divisors of 3354)
3354 / 3 = 1118 (the remainder is 0, so 3 and 1118 are divisors of 3354)
...
3354 / 56 = 59.892857142857 (the remainder is 50, so 56 is not a divisor of 3354)
3354 / 57 = 58.842105263158 (the remainder is 48, so 57 is not a divisor of 3354)