What are the divisors of 3348?

1, 2, 3, 4, 6, 9, 12, 18, 27, 31, 36, 54, 62, 93, 108, 124, 186, 279, 372, 558, 837, 1116, 1674, 3348

There is a total of 24 positive divisors.
The sum of these divisors is 8960.
The arithmetic mean is 373.33333333333.

16 even divisors

2, 4, 6, 12, 18, 36, 54, 62, 108, 124, 186, 372, 558, 1116, 1674, 3348

8 odd divisors

1, 3, 9, 27, 31, 93, 279, 837

How to compute the divisors of 3348?

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 3348 by each of the numbers from 1 to 3348 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)

3348 / 1 = 3348 (the remainder is 0, so 1 is a divisor of 3348)
3348 / 2 = 1674 (the remainder is 0, so 2 is a divisor of 3348)
3348 / 3 = 1116 (the remainder is 0, so 3 is a divisor of 3348)
...
3348 / 3347 = 1.0002987750224 (the remainder is 1, so 3347 is not a divisor of 3348)
3348 / 3348 = 1 (the remainder is 0, so 3348 is a divisor of 3348)

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 3348 (i.e. 57.861904565958). 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 $\frac{N}{d} = D$ )

3348 / 1 = 3348 (the remainder is 0, so 1 and 3348 are divisors of 3348)
3348 / 2 = 1674 (the remainder is 0, so 2 and 1674 are divisors of 3348)
3348 / 3 = 1116 (the remainder is 0, so 3 and 1116 are divisors of 3348)
...
3348 / 56 = 59.785714285714 (the remainder is 44, so 56 is not a divisor of 3348)
3348 / 57 = 58.736842105263 (the remainder is 42, so 57 is not a divisor of 3348)