What are the divisors of 4364?

1, 2, 4, 1091, 2182, 4364

There is a total of 6 positive divisors.
The sum of these divisors is 7644.
The arithmetic mean is 1274.

4 even divisors

2, 4, 2182, 4364

2 odd divisors

1, 1091

How to compute the divisors of 4364?

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 4364 by each of the numbers from 1 to 4364 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)

4364 / 1 = 4364 (the remainder is 0, so 1 is a divisor of 4364)
4364 / 2 = 2182 (the remainder is 0, so 2 is a divisor of 4364)
4364 / 3 = 1454.6666666667 (the remainder is 2, so 3 is not a divisor of 4364)
...
4364 / 4363 = 1.0002292000917 (the remainder is 1, so 4363 is not a divisor of 4364)
4364 / 4364 = 1 (the remainder is 0, so 4364 is a divisor of 4364)

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 4364 (i.e. 66.060578259655). 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 $\frac{N}{d} = D$ )

4364 / 1 = 4364 (the remainder is 0, so 1 and 4364 are divisors of 4364)
4364 / 2 = 2182 (the remainder is 0, so 2 and 2182 are divisors of 4364)
4364 / 3 = 1454.6666666667 (the remainder is 2, so 3 is not a divisor of 4364)
...
4364 / 65 = 67.138461538462 (the remainder is 9, so 65 is not a divisor of 4364)
4364 / 66 = 66.121212121212 (the remainder is 8, so 66 is not a divisor of 4364)