What are the divisors of 3148?

1, 2, 4, 787, 1574, 3148

There is a total of 6 positive divisors.
The sum of these divisors is 5516.
The arithmetic mean is 919.33333333333.

4 even divisors

2, 4, 1574, 3148

2 odd divisors

1, 787

How to compute the divisors of 3148?

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 3148 by each of the numbers from 1 to 3148 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)

3148 / 1 = 3148 (the remainder is 0, so 1 is a divisor of 3148)
3148 / 2 = 1574 (the remainder is 0, so 2 is a divisor of 3148)
3148 / 3 = 1049.3333333333 (the remainder is 1, so 3 is not a divisor of 3148)
...
3148 / 3147 = 1.0003177629488 (the remainder is 1, so 3147 is not a divisor of 3148)
3148 / 3148 = 1 (the remainder is 0, so 3148 is a divisor of 3148)

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 3148 (i.e. 56.107040556422). 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 $\frac{N}{d} = D$ )

3148 / 1 = 3148 (the remainder is 0, so 1 and 3148 are divisors of 3148)
3148 / 2 = 1574 (the remainder is 0, so 2 and 1574 are divisors of 3148)
3148 / 3 = 1049.3333333333 (the remainder is 1, so 3 is not a divisor of 3148)
...
3148 / 55 = 57.236363636364 (the remainder is 13, so 55 is not a divisor of 3148)
3148 / 56 = 56.214285714286 (the remainder is 12, so 56 is not a divisor of 3148)