What are the divisors of 3147?

1, 3, 1049, 3147

There is a total of 4 positive divisors.
The sum of these divisors is 4200.
The arithmetic mean is 1050.

4 odd divisors

1, 3, 1049, 3147

How to compute the divisors of 3147?

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 3147 by each of the numbers from 1 to 3147 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)

3147 / 1 = 3147 (the remainder is 0, so 1 is a divisor of 3147)
3147 / 2 = 1573.5 (the remainder is 1, so 2 is not a divisor of 3147)
3147 / 3 = 1049 (the remainder is 0, so 3 is a divisor of 3147)
...
3147 / 3146 = 1.0003178639542 (the remainder is 1, so 3146 is not a divisor of 3147)
3147 / 3147 = 1 (the remainder is 0, so 3147 is a divisor of 3147)

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 3147 (i.e. 56.098128311023). 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 $\frac{N}{d} = D$ )

3147 / 1 = 3147 (the remainder is 0, so 1 and 3147 are divisors of 3147)
3147 / 2 = 1573.5 (the remainder is 1, so 2 is not a divisor of 3147)
3147 / 3 = 1049 (the remainder is 0, so 3 and 1049 are divisors of 3147)
...
3147 / 55 = 57.218181818182 (the remainder is 12, so 55 is not a divisor of 3147)
3147 / 56 = 56.196428571429 (the remainder is 11, so 56 is not a divisor of 3147)