What are the divisors of 5951?

1, 11, 541, 5951

There is a total of 4 positive divisors.
The sum of these divisors is 6504.
The arithmetic mean is 1626.

4 odd divisors

1, 11, 541, 5951

How to compute the divisors of 5951?

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 5951 by each of the numbers from 1 to 5951 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)

5951 / 1 = 5951 (the remainder is 0, so 1 is a divisor of 5951)
5951 / 2 = 2975.5 (the remainder is 1, so 2 is not a divisor of 5951)
5951 / 3 = 1983.6666666667 (the remainder is 2, so 3 is not a divisor of 5951)
...
5951 / 5950 = 1.0001680672269 (the remainder is 1, so 5950 is not a divisor of 5951)
5951 / 5951 = 1 (the remainder is 0, so 5951 is a divisor of 5951)

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 5951 (i.e. 77.142724867611). 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 $\frac{N}{d} = D$ )

5951 / 1 = 5951 (the remainder is 0, so 1 and 5951 are divisors of 5951)
5951 / 2 = 2975.5 (the remainder is 1, so 2 is not a divisor of 5951)
5951 / 3 = 1983.6666666667 (the remainder is 2, so 3 is not a divisor of 5951)
...
5951 / 76 = 78.302631578947 (the remainder is 23, so 76 is not a divisor of 5951)
5951 / 77 = 77.285714285714 (the remainder is 22, so 77 is not a divisor of 5951)