What are the divisors of 4029?

1, 3, 17, 51, 79, 237, 1343, 4029

There is a total of 8 positive divisors.
The sum of these divisors is 5760.
The arithmetic mean is 720.

8 odd divisors

1, 3, 17, 51, 79, 237, 1343, 4029

How to compute the divisors of 4029?

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 4029 by each of the numbers from 1 to 4029 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)

4029 / 1 = 4029 (the remainder is 0, so 1 is a divisor of 4029)
4029 / 2 = 2014.5 (the remainder is 1, so 2 is not a divisor of 4029)
4029 / 3 = 1343 (the remainder is 0, so 3 is a divisor of 4029)
...
4029 / 4028 = 1.0002482621648 (the remainder is 1, so 4028 is not a divisor of 4029)
4029 / 4029 = 1 (the remainder is 0, so 4029 is a divisor of 4029)

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 4029 (i.e. 63.474404290233). 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 $\frac{N}{d} = D$ )

4029 / 1 = 4029 (the remainder is 0, so 1 and 4029 are divisors of 4029)
4029 / 2 = 2014.5 (the remainder is 1, so 2 is not a divisor of 4029)
4029 / 3 = 1343 (the remainder is 0, so 3 and 1343 are divisors of 4029)
...
4029 / 62 = 64.983870967742 (the remainder is 61, so 62 is not a divisor of 4029)
4029 / 63 = 63.952380952381 (the remainder is 60, so 63 is not a divisor of 4029)