What are the divisors of 1712?

1, 2, 4, 8, 16, 107, 214, 428, 856, 1712

There is a total of 10 positive divisors.
The sum of these divisors is 3348.
The arithmetic mean is 334.8.

8 even divisors

2, 4, 8, 16, 214, 428, 856, 1712

2 odd divisors

1, 107

How to compute the divisors of 1712?

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 1712 by each of the numbers from 1 to 1712 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)

1712 / 1 = 1712 (the remainder is 0, so 1 is a divisor of 1712)
1712 / 2 = 856 (the remainder is 0, so 2 is a divisor of 1712)
1712 / 3 = 570.66666666667 (the remainder is 2, so 3 is not a divisor of 1712)
...
1712 / 1711 = 1.0005844535359 (the remainder is 1, so 1711 is not a divisor of 1712)
1712 / 1712 = 1 (the remainder is 0, so 1712 is a divisor of 1712)

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 1712 (i.e. 41.376321731154). 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 $\frac{N}{d} = D$ )

1712 / 1 = 1712 (the remainder is 0, so 1 and 1712 are divisors of 1712)
1712 / 2 = 856 (the remainder is 0, so 2 and 856 are divisors of 1712)
1712 / 3 = 570.66666666667 (the remainder is 2, so 3 is not a divisor of 1712)
...
1712 / 40 = 42.8 (the remainder is 32, so 40 is not a divisor of 1712)
1712 / 41 = 41.756097560976 (the remainder is 31, so 41 is not a divisor of 1712)