What are the divisors of 5372?

1, 2, 4, 17, 34, 68, 79, 158, 316, 1343, 2686, 5372

There is a total of 12 positive divisors.
The sum of these divisors is 10080.
The arithmetic mean is 840.

8 even divisors

2, 4, 34, 68, 158, 316, 2686, 5372

4 odd divisors

1, 17, 79, 1343

How to compute the divisors of 5372?

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 5372 by each of the numbers from 1 to 5372 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)

5372 / 1 = 5372 (the remainder is 0, so 1 is a divisor of 5372)
5372 / 2 = 2686 (the remainder is 0, so 2 is a divisor of 5372)
5372 / 3 = 1790.6666666667 (the remainder is 2, so 3 is not a divisor of 5372)
...
5372 / 5371 = 1.000186185068 (the remainder is 1, so 5371 is not a divisor of 5372)
5372 / 5372 = 1 (the remainder is 0, so 5372 is a divisor of 5372)

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 5372 (i.e. 73.293928807235). 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 $\frac{N}{d} = D$ )

5372 / 1 = 5372 (the remainder is 0, so 1 and 5372 are divisors of 5372)
5372 / 2 = 2686 (the remainder is 0, so 2 and 2686 are divisors of 5372)
5372 / 3 = 1790.6666666667 (the remainder is 2, so 3 is not a divisor of 5372)
...
5372 / 72 = 74.611111111111 (the remainder is 44, so 72 is not a divisor of 5372)
5372 / 73 = 73.58904109589 (the remainder is 43, so 73 is not a divisor of 5372)