What are the divisors of 6051?

1, 3, 2017, 6051

There is a total of 4 positive divisors.
The sum of these divisors is 8072.
The arithmetic mean is 2018.

4 odd divisors

1, 3, 2017, 6051

How to compute the divisors of 6051?

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 6051 by each of the numbers from 1 to 6051 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)

6051 / 1 = 6051 (the remainder is 0, so 1 is a divisor of 6051)
6051 / 2 = 3025.5 (the remainder is 1, so 2 is not a divisor of 6051)
6051 / 3 = 2017 (the remainder is 0, so 3 is a divisor of 6051)
...
6051 / 6050 = 1.0001652892562 (the remainder is 1, so 6050 is not a divisor of 6051)
6051 / 6051 = 1 (the remainder is 0, so 6051 is a divisor of 6051)

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 6051 (i.e. 77.788173908378). 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 $\frac{N}{d} = D$ )

6051 / 1 = 6051 (the remainder is 0, so 1 and 6051 are divisors of 6051)
6051 / 2 = 3025.5 (the remainder is 1, so 2 is not a divisor of 6051)
6051 / 3 = 2017 (the remainder is 0, so 3 and 2017 are divisors of 6051)
...
6051 / 76 = 79.618421052632 (the remainder is 47, so 76 is not a divisor of 6051)
6051 / 77 = 78.584415584416 (the remainder is 45, so 77 is not a divisor of 6051)