What are the divisors of 2074?

1, 2, 17, 34, 61, 122, 1037, 2074

There is a total of 8 positive divisors.
The sum of these divisors is 3348.
The arithmetic mean is 418.5.

4 even divisors

2, 34, 122, 2074

4 odd divisors

1, 17, 61, 1037

How to compute the divisors of 2074?

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 2074 by each of the numbers from 1 to 2074 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)

2074 / 1 = 2074 (the remainder is 0, so 1 is a divisor of 2074)
2074 / 2 = 1037 (the remainder is 0, so 2 is a divisor of 2074)
2074 / 3 = 691.33333333333 (the remainder is 1, so 3 is not a divisor of 2074)
...
2074 / 2073 = 1.0004823926676 (the remainder is 1, so 2073 is not a divisor of 2074)
2074 / 2074 = 1 (the remainder is 0, so 2074 is a divisor of 2074)

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 2074 (i.e. 45.541190146943). 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 $\frac{N}{d} = D$ )

2074 / 1 = 2074 (the remainder is 0, so 1 and 2074 are divisors of 2074)
2074 / 2 = 1037 (the remainder is 0, so 2 and 1037 are divisors of 2074)
2074 / 3 = 691.33333333333 (the remainder is 1, so 3 is not a divisor of 2074)
...
2074 / 44 = 47.136363636364 (the remainder is 6, so 44 is not a divisor of 2074)
2074 / 45 = 46.088888888889 (the remainder is 4, so 45 is not a divisor of 2074)