What are the divisors of 5942?

1, 2, 2971, 5942

There is a total of 4 positive divisors.
The sum of these divisors is 8916.
The arithmetic mean is 2229.

2 even divisors

2, 5942

2 odd divisors

1, 2971

How to compute the divisors of 5942?

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 5942 by each of the numbers from 1 to 5942 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)

5942 / 1 = 5942 (the remainder is 0, so 1 is a divisor of 5942)
5942 / 2 = 2971 (the remainder is 0, so 2 is a divisor of 5942)
5942 / 3 = 1980.6666666667 (the remainder is 2, so 3 is not a divisor of 5942)
...
5942 / 5941 = 1.0001683218313 (the remainder is 1, so 5941 is not a divisor of 5942)
5942 / 5942 = 1 (the remainder is 0, so 5942 is a divisor of 5942)

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 5942 (i.e. 77.084369362407). 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 $\frac{N}{d} = D$ )

5942 / 1 = 5942 (the remainder is 0, so 1 and 5942 are divisors of 5942)
5942 / 2 = 2971 (the remainder is 0, so 2 and 2971 are divisors of 5942)
5942 / 3 = 1980.6666666667 (the remainder is 2, so 3 is not a divisor of 5942)
...
5942 / 76 = 78.184210526316 (the remainder is 14, so 76 is not a divisor of 5942)
5942 / 77 = 77.168831168831 (the remainder is 13, so 77 is not a divisor of 5942)