What are the divisors of 4162?

1, 2, 2081, 4162

There is a total of 4 positive divisors.
The sum of these divisors is 6246.
The arithmetic mean is 1561.5.

2 even divisors

2, 4162

2 odd divisors

1, 2081

How to compute the divisors of 4162?

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 4162 by each of the numbers from 1 to 4162 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)

4162 / 1 = 4162 (the remainder is 0, so 1 is a divisor of 4162)
4162 / 2 = 2081 (the remainder is 0, so 2 is a divisor of 4162)
4162 / 3 = 1387.3333333333 (the remainder is 1, so 3 is not a divisor of 4162)
...
4162 / 4161 = 1.0002403268445 (the remainder is 1, so 4161 is not a divisor of 4162)
4162 / 4162 = 1 (the remainder is 0, so 4162 is a divisor of 4162)

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 4162 (i.e. 64.513564465157). 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 $\frac{N}{d} = D$ )

4162 / 1 = 4162 (the remainder is 0, so 1 and 4162 are divisors of 4162)
4162 / 2 = 2081 (the remainder is 0, so 2 and 2081 are divisors of 4162)
4162 / 3 = 1387.3333333333 (the remainder is 1, so 3 is not a divisor of 4162)
...
4162 / 63 = 66.063492063492 (the remainder is 4, so 63 is not a divisor of 4162)
4162 / 64 = 65.03125 (the remainder is 2, so 64 is not a divisor of 4162)