What are the divisors of 3119?

1, 3119

There is a total of 2 positive divisors.
The sum of these divisors is 3120.
The arithmetic mean is 1560.

2 odd divisors

1, 3119

How to compute the divisors of 3119?

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 3119 by each of the numbers from 1 to 3119 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)

3119 / 1 = 3119 (the remainder is 0, so 1 is a divisor of 3119)
3119 / 2 = 1559.5 (the remainder is 1, so 2 is not a divisor of 3119)
3119 / 3 = 1039.6666666667 (the remainder is 2, so 3 is not a divisor of 3119)
...
3119 / 3118 = 1.0003207184092 (the remainder is 1, so 3118 is not a divisor of 3119)
3119 / 3119 = 1 (the remainder is 0, so 3119 is a divisor of 3119)

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 3119 (i.e. 55.848008021773). 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 $\frac{N}{d} = D$ )

3119 / 1 = 3119 (the remainder is 0, so 1 and 3119 are divisors of 3119)
3119 / 2 = 1559.5 (the remainder is 1, so 2 is not a divisor of 3119)
3119 / 3 = 1039.6666666667 (the remainder is 2, so 3 is not a divisor of 3119)
...
3119 / 54 = 57.759259259259 (the remainder is 41, so 54 is not a divisor of 3119)
3119 / 55 = 56.709090909091 (the remainder is 39, so 55 is not a divisor of 3119)