What are the divisors of 4114?

1, 2, 11, 17, 22, 34, 121, 187, 242, 374, 2057, 4114

There is a total of 12 positive divisors.
The sum of these divisors is 7182.
The arithmetic mean is 598.5.

6 even divisors

2, 22, 34, 242, 374, 4114

6 odd divisors

1, 11, 17, 121, 187, 2057

How to compute the divisors of 4114?

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 4114 by each of the numbers from 1 to 4114 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)

4114 / 1 = 4114 (the remainder is 0, so 1 is a divisor of 4114)
4114 / 2 = 2057 (the remainder is 0, so 2 is a divisor of 4114)
4114 / 3 = 1371.3333333333 (the remainder is 1, so 3 is not a divisor of 4114)
...
4114 / 4113 = 1.0002431315342 (the remainder is 1, so 4113 is not a divisor of 4114)
4114 / 4114 = 1 (the remainder is 0, so 4114 is a divisor of 4114)

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 4114 (i.e. 64.140470843298). 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 $\frac{N}{d} = D$ )

4114 / 1 = 4114 (the remainder is 0, so 1 and 4114 are divisors of 4114)
4114 / 2 = 2057 (the remainder is 0, so 2 and 2057 are divisors of 4114)
4114 / 3 = 1371.3333333333 (the remainder is 1, so 3 is not a divisor of 4114)
...
4114 / 63 = 65.301587301587 (the remainder is 19, so 63 is not a divisor of 4114)
4114 / 64 = 64.28125 (the remainder is 18, so 64 is not a divisor of 4114)