What are the divisors of 5973?

1, 3, 11, 33, 181, 543, 1991, 5973

There is a total of 8 positive divisors.
The sum of these divisors is 8736.
The arithmetic mean is 1092.

8 odd divisors

1, 3, 11, 33, 181, 543, 1991, 5973

How to compute the divisors of 5973?

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 5973 by each of the numbers from 1 to 5973 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)

5973 / 1 = 5973 (the remainder is 0, so 1 is a divisor of 5973)
5973 / 2 = 2986.5 (the remainder is 1, so 2 is not a divisor of 5973)
5973 / 3 = 1991 (the remainder is 0, so 3 is a divisor of 5973)
...
5973 / 5972 = 1.0001674480911 (the remainder is 1, so 5972 is not a divisor of 5973)
5973 / 5973 = 1 (the remainder is 0, so 5973 is a divisor of 5973)

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 5973 (i.e. 77.285186161385). 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 $\frac{N}{d} = D$ )

5973 / 1 = 5973 (the remainder is 0, so 1 and 5973 are divisors of 5973)
5973 / 2 = 2986.5 (the remainder is 1, so 2 is not a divisor of 5973)
5973 / 3 = 1991 (the remainder is 0, so 3 and 1991 are divisors of 5973)
...
5973 / 76 = 78.592105263158 (the remainder is 45, so 76 is not a divisor of 5973)
5973 / 77 = 77.571428571429 (the remainder is 44, so 77 is not a divisor of 5973)