What are the divisors of 4074?

1, 2, 3, 6, 7, 14, 21, 42, 97, 194, 291, 582, 679, 1358, 2037, 4074

There is a total of 16 positive divisors.
The sum of these divisors is 9408.
The arithmetic mean is 588.

8 even divisors

2, 6, 14, 42, 194, 582, 1358, 4074

8 odd divisors

1, 3, 7, 21, 97, 291, 679, 2037

How to compute the divisors of 4074?

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 4074 by each of the numbers from 1 to 4074 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)

4074 / 1 = 4074 (the remainder is 0, so 1 is a divisor of 4074)
4074 / 2 = 2037 (the remainder is 0, so 2 is a divisor of 4074)
4074 / 3 = 1358 (the remainder is 0, so 3 is a divisor of 4074)
...
4074 / 4073 = 1.0002455192733 (the remainder is 1, so 4073 is not a divisor of 4074)
4074 / 4074 = 1 (the remainder is 0, so 4074 is a divisor of 4074)

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 4074 (i.e. 63.827893588932). 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 $\frac{N}{d} = D$ )

4074 / 1 = 4074 (the remainder is 0, so 1 and 4074 are divisors of 4074)
4074 / 2 = 2037 (the remainder is 0, so 2 and 2037 are divisors of 4074)
4074 / 3 = 1358 (the remainder is 0, so 3 and 1358 are divisors of 4074)
...
4074 / 62 = 65.709677419355 (the remainder is 44, so 62 is not a divisor of 4074)
4074 / 63 = 64.666666666667 (the remainder is 42, so 63 is not a divisor of 4074)