What are the divisors of 4146?

1, 2, 3, 6, 691, 1382, 2073, 4146

There is a total of 8 positive divisors.
The sum of these divisors is 8304.
The arithmetic mean is 1038.

4 even divisors

2, 6, 1382, 4146

4 odd divisors

1, 3, 691, 2073

How to compute the divisors of 4146?

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 4146 by each of the numbers from 1 to 4146 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)

4146 / 1 = 4146 (the remainder is 0, so 1 is a divisor of 4146)
4146 / 2 = 2073 (the remainder is 0, so 2 is a divisor of 4146)
4146 / 3 = 1382 (the remainder is 0, so 3 is a divisor of 4146)
...
4146 / 4145 = 1.0002412545235 (the remainder is 1, so 4145 is not a divisor of 4146)
4146 / 4146 = 1 (the remainder is 0, so 4146 is a divisor of 4146)

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 4146 (i.e. 64.389440128021). 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 $\frac{N}{d} = D$ )

4146 / 1 = 4146 (the remainder is 0, so 1 and 4146 are divisors of 4146)
4146 / 2 = 2073 (the remainder is 0, so 2 and 2073 are divisors of 4146)
4146 / 3 = 1382 (the remainder is 0, so 3 and 1382 are divisors of 4146)
...
4146 / 63 = 65.809523809524 (the remainder is 51, so 63 is not a divisor of 4146)
4146 / 64 = 64.78125 (the remainder is 50, so 64 is not a divisor of 4146)