What are the divisors of 2076?

1, 2, 3, 4, 6, 12, 173, 346, 519, 692, 1038, 2076

There is a total of 12 positive divisors.
The sum of these divisors is 4872.
The arithmetic mean is 406.

8 even divisors

2, 4, 6, 12, 346, 692, 1038, 2076

4 odd divisors

1, 3, 173, 519

How to compute the divisors of 2076?

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 2076 by each of the numbers from 1 to 2076 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)

2076 / 1 = 2076 (the remainder is 0, so 1 is a divisor of 2076)
2076 / 2 = 1038 (the remainder is 0, so 2 is a divisor of 2076)
2076 / 3 = 692 (the remainder is 0, so 3 is a divisor of 2076)
...
2076 / 2075 = 1.0004819277108 (the remainder is 1, so 2075 is not a divisor of 2076)
2076 / 2076 = 1 (the remainder is 0, so 2076 is a divisor of 2076)

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 2076 (i.e. 45.563142999578). 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 $\frac{N}{d} = D$ )

2076 / 1 = 2076 (the remainder is 0, so 1 and 2076 are divisors of 2076)
2076 / 2 = 1038 (the remainder is 0, so 2 and 1038 are divisors of 2076)
2076 / 3 = 692 (the remainder is 0, so 3 and 692 are divisors of 2076)
...
2076 / 44 = 47.181818181818 (the remainder is 8, so 44 is not a divisor of 2076)
2076 / 45 = 46.133333333333 (the remainder is 6, so 45 is not a divisor of 2076)