What are the divisors of 1876?

1, 2, 4, 7, 14, 28, 67, 134, 268, 469, 938, 1876

There is a total of 12 positive divisors.
The sum of these divisors is 3808.
The arithmetic mean is 317.33333333333.

8 even divisors

2, 4, 14, 28, 134, 268, 938, 1876

4 odd divisors

1, 7, 67, 469

How to compute the divisors of 1876?

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 1876 by each of the numbers from 1 to 1876 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)

1876 / 1 = 1876 (the remainder is 0, so 1 is a divisor of 1876)
1876 / 2 = 938 (the remainder is 0, so 2 is a divisor of 1876)
1876 / 3 = 625.33333333333 (the remainder is 1, so 3 is not a divisor of 1876)
...
1876 / 1875 = 1.0005333333333 (the remainder is 1, so 1875 is not a divisor of 1876)
1876 / 1876 = 1 (the remainder is 0, so 1876 is a divisor of 1876)

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 1876 (i.e. 43.312815655415). 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 $\frac{N}{d} = D$ )

1876 / 1 = 1876 (the remainder is 0, so 1 and 1876 are divisors of 1876)
1876 / 2 = 938 (the remainder is 0, so 2 and 938 are divisors of 1876)
1876 / 3 = 625.33333333333 (the remainder is 1, so 3 is not a divisor of 1876)
...
1876 / 42 = 44.666666666667 (the remainder is 28, so 42 is not a divisor of 1876)
1876 / 43 = 43.627906976744 (the remainder is 27, so 43 is not a divisor of 1876)