What are the divisors of 5972?

1, 2, 4, 1493, 2986, 5972

There is a total of 6 positive divisors.
The sum of these divisors is 10458.
The arithmetic mean is 1743.

4 even divisors

2, 4, 2986, 5972

2 odd divisors

1, 1493

How to compute the divisors of 5972?

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 5972 by each of the numbers from 1 to 5972 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)

5972 / 1 = 5972 (the remainder is 0, so 1 is a divisor of 5972)
5972 / 2 = 2986 (the remainder is 0, so 2 is a divisor of 5972)
5972 / 3 = 1990.6666666667 (the remainder is 2, so 3 is not a divisor of 5972)
...
5972 / 5971 = 1.0001674761347 (the remainder is 1, so 5971 is not a divisor of 5972)
5972 / 5972 = 1 (the remainder is 0, so 5972 is a divisor of 5972)

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 5972 (i.e. 77.278716345447). 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 $\frac{N}{d} = D$ )

5972 / 1 = 5972 (the remainder is 0, so 1 and 5972 are divisors of 5972)
5972 / 2 = 2986 (the remainder is 0, so 2 and 2986 are divisors of 5972)
5972 / 3 = 1990.6666666667 (the remainder is 2, so 3 is not a divisor of 5972)
...
5972 / 76 = 78.578947368421 (the remainder is 44, so 76 is not a divisor of 5972)
5972 / 77 = 77.558441558442 (the remainder is 43, so 77 is not a divisor of 5972)