What are the divisors of 2054?

1, 2, 13, 26, 79, 158, 1027, 2054

There is a total of 8 positive divisors.
The sum of these divisors is 3360.
The arithmetic mean is 420.

4 even divisors

2, 26, 158, 2054

4 odd divisors

1, 13, 79, 1027

How to compute the divisors of 2054?

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 2054 by each of the numbers from 1 to 2054 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)

2054 / 1 = 2054 (the remainder is 0, so 1 is a divisor of 2054)
2054 / 2 = 1027 (the remainder is 0, so 2 is a divisor of 2054)
2054 / 3 = 684.66666666667 (the remainder is 2, so 3 is not a divisor of 2054)
...
2054 / 2053 = 1.0004870920604 (the remainder is 1, so 2053 is not a divisor of 2054)
2054 / 2054 = 1 (the remainder is 0, so 2054 is a divisor of 2054)

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 2054 (i.e. 45.321076774499). 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 $\frac{N}{d} = D$ )

2054 / 1 = 2054 (the remainder is 0, so 1 and 2054 are divisors of 2054)
2054 / 2 = 1027 (the remainder is 0, so 2 and 1027 are divisors of 2054)
2054 / 3 = 684.66666666667 (the remainder is 2, so 3 is not a divisor of 2054)
...
2054 / 44 = 46.681818181818 (the remainder is 30, so 44 is not a divisor of 2054)
2054 / 45 = 45.644444444444 (the remainder is 29, so 45 is not a divisor of 2054)