What are the divisors of 3100?

1, 2, 4, 5, 10, 20, 25, 31, 50, 62, 100, 124, 155, 310, 620, 775, 1550, 3100

There is a total of 18 positive divisors.
The sum of these divisors is 6944.
The arithmetic mean is 385.77777777778.

12 even divisors

2, 4, 10, 20, 50, 62, 100, 124, 310, 620, 1550, 3100

6 odd divisors

1, 5, 25, 31, 155, 775

How to compute the divisors of 3100?

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 3100 by each of the numbers from 1 to 3100 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)

3100 / 1 = 3100 (the remainder is 0, so 1 is a divisor of 3100)
3100 / 2 = 1550 (the remainder is 0, so 2 is a divisor of 3100)
3100 / 3 = 1033.3333333333 (the remainder is 1, so 3 is not a divisor of 3100)
...
3100 / 3099 = 1.000322684737 (the remainder is 1, so 3099 is not a divisor of 3100)
3100 / 3100 = 1 (the remainder is 0, so 3100 is a divisor of 3100)

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 3100 (i.e. 55.6776436283). 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 $\frac{N}{d} = D$ )

3100 / 1 = 3100 (the remainder is 0, so 1 and 3100 are divisors of 3100)
3100 / 2 = 1550 (the remainder is 0, so 2 and 1550 are divisors of 3100)
3100 / 3 = 1033.3333333333 (the remainder is 1, so 3 is not a divisor of 3100)
...
3100 / 54 = 57.407407407407 (the remainder is 22, so 54 is not a divisor of 3100)
3100 / 55 = 56.363636363636 (the remainder is 20, so 55 is not a divisor of 3100)