What are the divisors of 3026?

1, 2, 17, 34, 89, 178, 1513, 3026

There is a total of 8 positive divisors.
The sum of these divisors is 4860.
The arithmetic mean is 607.5.

4 even divisors

2, 34, 178, 3026

4 odd divisors

1, 17, 89, 1513

How to compute the divisors of 3026?

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 3026 by each of the numbers from 1 to 3026 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)

3026 / 1 = 3026 (the remainder is 0, so 1 is a divisor of 3026)
3026 / 2 = 1513 (the remainder is 0, so 2 is a divisor of 3026)
3026 / 3 = 1008.6666666667 (the remainder is 2, so 3 is not a divisor of 3026)
...
3026 / 3025 = 1.0003305785124 (the remainder is 1, so 3025 is not a divisor of 3026)
3026 / 3026 = 1 (the remainder is 0, so 3026 is a divisor of 3026)

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 3026 (i.e. 55.0090901579). 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 $\frac{N}{d} = D$ )

3026 / 1 = 3026 (the remainder is 0, so 1 and 3026 are divisors of 3026)
3026 / 2 = 1513 (the remainder is 0, so 2 and 1513 are divisors of 3026)
3026 / 3 = 1008.6666666667 (the remainder is 2, so 3 is not a divisor of 3026)
...
3026 / 54 = 56.037037037037 (the remainder is 2, so 54 is not a divisor of 3026)
3026 / 55 = 55.018181818182 (the remainder is 1, so 55 is not a divisor of 3026)