What are the divisors of 6162?

1, 2, 3, 6, 13, 26, 39, 78, 79, 158, 237, 474, 1027, 2054, 3081, 6162

There is a total of 16 positive divisors.
The sum of these divisors is 13440.
The arithmetic mean is 840.

8 even divisors

2, 6, 26, 78, 158, 474, 2054, 6162

8 odd divisors

1, 3, 13, 39, 79, 237, 1027, 3081

How to compute the divisors of 6162?

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 6162 by each of the numbers from 1 to 6162 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)

6162 / 1 = 6162 (the remainder is 0, so 1 is a divisor of 6162)
6162 / 2 = 3081 (the remainder is 0, so 2 is a divisor of 6162)
6162 / 3 = 2054 (the remainder is 0, so 3 is a divisor of 6162)
...
6162 / 6161 = 1.0001623113131 (the remainder is 1, so 6161 is not a divisor of 6162)
6162 / 6162 = 1 (the remainder is 0, so 6162 is a divisor of 6162)

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 6162 (i.e. 78.498407627161). 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 $\frac{N}{d} = D$ )

6162 / 1 = 6162 (the remainder is 0, so 1 and 6162 are divisors of 6162)
6162 / 2 = 3081 (the remainder is 0, so 2 and 3081 are divisors of 6162)
6162 / 3 = 2054 (the remainder is 0, so 3 and 2054 are divisors of 6162)
...
6162 / 77 = 80.025974025974 (the remainder is 2, so 77 is not a divisor of 6162)
6162 / 78 = 79 (the remainder is 0, so 78 and 79 are divisors of 6162)