What are the divisors of 3137?

1, 3137

There is a total of 2 positive divisors.
The sum of these divisors is 3138.
The arithmetic mean is 1569.

2 odd divisors

1, 3137

How to compute the divisors of 3137?

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 3137 by each of the numbers from 1 to 3137 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)

3137 / 1 = 3137 (the remainder is 0, so 1 is a divisor of 3137)
3137 / 2 = 1568.5 (the remainder is 1, so 2 is not a divisor of 3137)
3137 / 3 = 1045.6666666667 (the remainder is 2, so 3 is not a divisor of 3137)
...
3137 / 3136 = 1.000318877551 (the remainder is 1, so 3136 is not a divisor of 3137)
3137 / 3137 = 1 (the remainder is 0, so 3137 is a divisor of 3137)

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 3137 (i.e. 56.008927859762). 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 $\frac{N}{d} = D$ )

3137 / 1 = 3137 (the remainder is 0, so 1 and 3137 are divisors of 3137)
3137 / 2 = 1568.5 (the remainder is 1, so 2 is not a divisor of 3137)
3137 / 3 = 1045.6666666667 (the remainder is 2, so 3 is not a divisor of 3137)
...
3137 / 55 = 57.036363636364 (the remainder is 2, so 55 is not a divisor of 3137)
3137 / 56 = 56.017857142857 (the remainder is 1, so 56 is not a divisor of 3137)