What are the divisors of 4316?

1, 2, 4, 13, 26, 52, 83, 166, 332, 1079, 2158, 4316

There is a total of 12 positive divisors.
The sum of these divisors is 8232.
The arithmetic mean is 686.

8 even divisors

2, 4, 26, 52, 166, 332, 2158, 4316

4 odd divisors

1, 13, 83, 1079

How to compute the divisors of 4316?

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 4316 by each of the numbers from 1 to 4316 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)

4316 / 1 = 4316 (the remainder is 0, so 1 is a divisor of 4316)
4316 / 2 = 2158 (the remainder is 0, so 2 is a divisor of 4316)
4316 / 3 = 1438.6666666667 (the remainder is 2, so 3 is not a divisor of 4316)
...
4316 / 4315 = 1.0002317497103 (the remainder is 1, so 4315 is not a divisor of 4316)
4316 / 4316 = 1 (the remainder is 0, so 4316 is a divisor of 4316)

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 4316 (i.e. 65.696270822627). 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 $\frac{N}{d} = D$ )

4316 / 1 = 4316 (the remainder is 0, so 1 and 4316 are divisors of 4316)
4316 / 2 = 2158 (the remainder is 0, so 2 and 2158 are divisors of 4316)
4316 / 3 = 1438.6666666667 (the remainder is 2, so 3 is not a divisor of 4316)
...
4316 / 64 = 67.4375 (the remainder is 28, so 64 is not a divisor of 4316)
4316 / 65 = 66.4 (the remainder is 26, so 65 is not a divisor of 4316)