What are the divisors of 4102?

1, 2, 7, 14, 293, 586, 2051, 4102

There is a total of 8 positive divisors.
The sum of these divisors is 7056.
The arithmetic mean is 882.

4 even divisors

2, 14, 586, 4102

4 odd divisors

1, 7, 293, 2051

How to compute the divisors of 4102?

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 4102 by each of the numbers from 1 to 4102 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)

4102 / 1 = 4102 (the remainder is 0, so 1 is a divisor of 4102)
4102 / 2 = 2051 (the remainder is 0, so 2 is a divisor of 4102)
4102 / 3 = 1367.3333333333 (the remainder is 1, so 3 is not a divisor of 4102)
...
4102 / 4101 = 1.0002438429651 (the remainder is 1, so 4101 is not a divisor of 4102)
4102 / 4102 = 1 (the remainder is 0, so 4102 is a divisor of 4102)

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 4102 (i.e. 64.046857846424). 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 $\frac{N}{d} = D$ )

4102 / 1 = 4102 (the remainder is 0, so 1 and 4102 are divisors of 4102)
4102 / 2 = 2051 (the remainder is 0, so 2 and 2051 are divisors of 4102)
4102 / 3 = 1367.3333333333 (the remainder is 1, so 3 is not a divisor of 4102)
...
4102 / 63 = 65.111111111111 (the remainder is 7, so 63 is not a divisor of 4102)
4102 / 64 = 64.09375 (the remainder is 6, so 64 is not a divisor of 4102)