What are the divisors of 3149?

1, 47, 67, 3149

There is a total of 4 positive divisors.
The sum of these divisors is 3264.
The arithmetic mean is 816.

4 odd divisors

1, 47, 67, 3149

How to compute the divisors of 3149?

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 3149 by each of the numbers from 1 to 3149 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)

3149 / 1 = 3149 (the remainder is 0, so 1 is a divisor of 3149)
3149 / 2 = 1574.5 (the remainder is 1, so 2 is not a divisor of 3149)
3149 / 3 = 1049.6666666667 (the remainder is 2, so 3 is not a divisor of 3149)
...
3149 / 3148 = 1.0003176620076 (the remainder is 1, so 3148 is not a divisor of 3149)
3149 / 3149 = 1 (the remainder is 0, so 3149 is a divisor of 3149)

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 3149 (i.e. 56.115951386393). 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 $\frac{N}{d} = D$ )

3149 / 1 = 3149 (the remainder is 0, so 1 and 3149 are divisors of 3149)
3149 / 2 = 1574.5 (the remainder is 1, so 2 is not a divisor of 3149)
3149 / 3 = 1049.6666666667 (the remainder is 2, so 3 is not a divisor of 3149)
...
3149 / 55 = 57.254545454545 (the remainder is 14, so 55 is not a divisor of 3149)
3149 / 56 = 56.232142857143 (the remainder is 13, so 56 is not a divisor of 3149)