What are the divisors of 2026?

1, 2, 1013, 2026

There is a total of 4 positive divisors.
The sum of these divisors is 3042.
The arithmetic mean is 760.5.

2 even divisors

2, 2026

2 odd divisors

1, 1013

How to compute the divisors of 2026?

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 2026 by each of the numbers from 1 to 2026 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)

2026 / 1 = 2026 (the remainder is 0, so 1 is a divisor of 2026)
2026 / 2 = 1013 (the remainder is 0, so 2 is a divisor of 2026)
2026 / 3 = 675.33333333333 (the remainder is 1, so 3 is not a divisor of 2026)
...
2026 / 2025 = 1.0004938271605 (the remainder is 1, so 2025 is not a divisor of 2026)
2026 / 2026 = 1 (the remainder is 0, so 2026 is a divisor of 2026)

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 2026 (i.e. 45.011109739708). 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 $\frac{N}{d} = D$ )

2026 / 1 = 2026 (the remainder is 0, so 1 and 2026 are divisors of 2026)
2026 / 2 = 1013 (the remainder is 0, so 2 and 1013 are divisors of 2026)
2026 / 3 = 675.33333333333 (the remainder is 1, so 3 is not a divisor of 2026)
...
2026 / 44 = 46.045454545455 (the remainder is 2, so 44 is not a divisor of 2026)
2026 / 45 = 45.022222222222 (the remainder is 1, so 45 is not a divisor of 2026)