What are the divisors of 5948?

1, 2, 4, 1487, 2974, 5948

There is a total of 6 positive divisors.
The sum of these divisors is 10416.
The arithmetic mean is 1736.

4 even divisors

2, 4, 2974, 5948

2 odd divisors

1, 1487

How to compute the divisors of 5948?

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 5948 by each of the numbers from 1 to 5948 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)

5948 / 1 = 5948 (the remainder is 0, so 1 is a divisor of 5948)
5948 / 2 = 2974 (the remainder is 0, so 2 is a divisor of 5948)
5948 / 3 = 1982.6666666667 (the remainder is 2, so 3 is not a divisor of 5948)
...
5948 / 5947 = 1.0001681520094 (the remainder is 1, so 5947 is not a divisor of 5948)
5948 / 5948 = 1 (the remainder is 0, so 5948 is a divisor of 5948)

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 5948 (i.e. 77.123277938635). 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 $\frac{N}{d} = D$ )

5948 / 1 = 5948 (the remainder is 0, so 1 and 5948 are divisors of 5948)
5948 / 2 = 2974 (the remainder is 0, so 2 and 2974 are divisors of 5948)
5948 / 3 = 1982.6666666667 (the remainder is 2, so 3 is not a divisor of 5948)
...
5948 / 76 = 78.263157894737 (the remainder is 20, so 76 is not a divisor of 5948)
5948 / 77 = 77.246753246753 (the remainder is 19, so 77 is not a divisor of 5948)