What are the divisors of 2114?

1, 2, 7, 14, 151, 302, 1057, 2114

There is a total of 8 positive divisors.
The sum of these divisors is 3648.
The arithmetic mean is 456.

4 even divisors

2, 14, 302, 2114

4 odd divisors

1, 7, 151, 1057

How to compute the divisors of 2114?

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 2114 by each of the numbers from 1 to 2114 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)

2114 / 1 = 2114 (the remainder is 0, so 1 is a divisor of 2114)
2114 / 2 = 1057 (the remainder is 0, so 2 is a divisor of 2114)
2114 / 3 = 704.66666666667 (the remainder is 2, so 3 is not a divisor of 2114)
...
2114 / 2113 = 1.0004732607667 (the remainder is 1, so 2113 is not a divisor of 2114)
2114 / 2114 = 1 (the remainder is 0, so 2114 is a divisor of 2114)

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 2114 (i.e. 45.978255730291). 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 $\frac{N}{d} = D$ )

2114 / 1 = 2114 (the remainder is 0, so 1 and 2114 are divisors of 2114)
2114 / 2 = 1057 (the remainder is 0, so 2 and 1057 are divisors of 2114)
2114 / 3 = 704.66666666667 (the remainder is 2, so 3 is not a divisor of 2114)
...
2114 / 44 = 48.045454545455 (the remainder is 2, so 44 is not a divisor of 2114)
2114 / 45 = 46.977777777778 (the remainder is 44, so 45 is not a divisor of 2114)