What are the divisors of 5921?

1, 31, 191, 5921

There is a total of 4 positive divisors.
The sum of these divisors is 6144.
The arithmetic mean is 1536.

4 odd divisors

1, 31, 191, 5921

How to compute the divisors of 5921?

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 5921 by each of the numbers from 1 to 5921 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)

5921 / 1 = 5921 (the remainder is 0, so 1 is a divisor of 5921)
5921 / 2 = 2960.5 (the remainder is 1, so 2 is not a divisor of 5921)
5921 / 3 = 1973.6666666667 (the remainder is 2, so 3 is not a divisor of 5921)
...
5921 / 5920 = 1.0001689189189 (the remainder is 1, so 5920 is not a divisor of 5921)
5921 / 5921 = 1 (the remainder is 0, so 5921 is a divisor of 5921)

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 5921 (i.e. 76.948034412843). 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 $\frac{N}{d} = D$ )

5921 / 1 = 5921 (the remainder is 0, so 1 and 5921 are divisors of 5921)
5921 / 2 = 2960.5 (the remainder is 1, so 2 is not a divisor of 5921)
5921 / 3 = 1973.6666666667 (the remainder is 2, so 3 is not a divisor of 5921)
...
5921 / 75 = 78.946666666667 (the remainder is 71, so 75 is not a divisor of 5921)
5921 / 76 = 77.907894736842 (the remainder is 69, so 76 is not a divisor of 5921)