What are the divisors of 4188?

1, 2, 3, 4, 6, 12, 349, 698, 1047, 1396, 2094, 4188

There is a total of 12 positive divisors.
The sum of these divisors is 9800.
The arithmetic mean is 816.66666666667.

8 even divisors

2, 4, 6, 12, 698, 1396, 2094, 4188

4 odd divisors

1, 3, 349, 1047

How to compute the divisors of 4188?

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 4188 by each of the numbers from 1 to 4188 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)

4188 / 1 = 4188 (the remainder is 0, so 1 is a divisor of 4188)
4188 / 2 = 2094 (the remainder is 0, so 2 is a divisor of 4188)
4188 / 3 = 1396 (the remainder is 0, so 3 is a divisor of 4188)
...
4188 / 4187 = 1.0002388344877 (the remainder is 1, so 4187 is not a divisor of 4188)
4188 / 4188 = 1 (the remainder is 0, so 4188 is a divisor of 4188)

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 4188 (i.e. 64.714758749454). 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 $\frac{N}{d} = D$ )

4188 / 1 = 4188 (the remainder is 0, so 1 and 4188 are divisors of 4188)
4188 / 2 = 2094 (the remainder is 0, so 2 and 2094 are divisors of 4188)
4188 / 3 = 1396 (the remainder is 0, so 3 and 1396 are divisors of 4188)
...
4188 / 63 = 66.47619047619 (the remainder is 30, so 63 is not a divisor of 4188)
4188 / 64 = 65.4375 (the remainder is 28, so 64 is not a divisor of 4188)