What are the divisors of 4372?

1, 2, 4, 1093, 2186, 4372

There is a total of 6 positive divisors.
The sum of these divisors is 7658.
The arithmetic mean is 1276.3333333333.

4 even divisors

2, 4, 2186, 4372

2 odd divisors

1, 1093

How to compute the divisors of 4372?

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 4372 by each of the numbers from 1 to 4372 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)

4372 / 1 = 4372 (the remainder is 0, so 1 is a divisor of 4372)
4372 / 2 = 2186 (the remainder is 0, so 2 is a divisor of 4372)
4372 / 3 = 1457.3333333333 (the remainder is 1, so 3 is not a divisor of 4372)
...
4372 / 4371 = 1.0002287805994 (the remainder is 1, so 4371 is not a divisor of 4372)
4372 / 4372 = 1 (the remainder is 0, so 4372 is a divisor of 4372)

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 4372 (i.e. 66.121101019266). 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 $\frac{N}{d} = D$ )

4372 / 1 = 4372 (the remainder is 0, so 1 and 4372 are divisors of 4372)
4372 / 2 = 2186 (the remainder is 0, so 2 and 2186 are divisors of 4372)
4372 / 3 = 1457.3333333333 (the remainder is 1, so 3 is not a divisor of 4372)
...
4372 / 65 = 67.261538461538 (the remainder is 17, so 65 is not a divisor of 4372)
4372 / 66 = 66.242424242424 (the remainder is 16, so 66 is not a divisor of 4372)