What are the divisors of 1676?

1, 2, 4, 419, 838, 1676

There is a total of 6 positive divisors.
The sum of these divisors is 2940.
The arithmetic mean is 490.

4 even divisors

2, 4, 838, 1676

2 odd divisors

1, 419

How to compute the divisors of 1676?

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 1676 by each of the numbers from 1 to 1676 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)

1676 / 1 = 1676 (the remainder is 0, so 1 is a divisor of 1676)
1676 / 2 = 838 (the remainder is 0, so 2 is a divisor of 1676)
1676 / 3 = 558.66666666667 (the remainder is 2, so 3 is not a divisor of 1676)
...
1676 / 1675 = 1.0005970149254 (the remainder is 1, so 1675 is not a divisor of 1676)
1676 / 1676 = 1 (the remainder is 0, so 1676 is a divisor of 1676)

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 1676 (i.e. 40.938978980917). 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 $\frac{N}{d} = D$ )

1676 / 1 = 1676 (the remainder is 0, so 1 and 1676 are divisors of 1676)
1676 / 2 = 838 (the remainder is 0, so 2 and 838 are divisors of 1676)
1676 / 3 = 558.66666666667 (the remainder is 2, so 3 is not a divisor of 1676)
...
1676 / 39 = 42.974358974359 (the remainder is 38, so 39 is not a divisor of 1676)
1676 / 40 = 41.9 (the remainder is 36, so 40 is not a divisor of 1676)