What are the divisors of 5926?

1, 2, 2963, 5926

There is a total of 4 positive divisors.
The sum of these divisors is 8892.
The arithmetic mean is 2223.

2 even divisors

2, 5926

2 odd divisors

1, 2963

How to compute the divisors of 5926?

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 5926 by each of the numbers from 1 to 5926 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)

5926 / 1 = 5926 (the remainder is 0, so 1 is a divisor of 5926)
5926 / 2 = 2963 (the remainder is 0, so 2 is a divisor of 5926)
5926 / 3 = 1975.3333333333 (the remainder is 1, so 3 is not a divisor of 5926)
...
5926 / 5925 = 1.0001687763713 (the remainder is 1, so 5925 is not a divisor of 5926)
5926 / 5926 = 1 (the remainder is 0, so 5926 is a divisor of 5926)

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 5926 (i.e. 76.980517015671). 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 $\frac{N}{d} = D$ )

5926 / 1 = 5926 (the remainder is 0, so 1 and 5926 are divisors of 5926)
5926 / 2 = 2963 (the remainder is 0, so 2 and 2963 are divisors of 5926)
5926 / 3 = 1975.3333333333 (the remainder is 1, so 3 is not a divisor of 5926)
...
5926 / 75 = 79.013333333333 (the remainder is 1, so 75 is not a divisor of 5926)
5926 / 76 = 77.973684210526 (the remainder is 74, so 76 is not a divisor of 5926)