What are the divisors of 1714?

1, 2, 857, 1714

There is a total of 4 positive divisors.
The sum of these divisors is 2574.
The arithmetic mean is 643.5.

2 even divisors

2, 1714

2 odd divisors

1, 857

How to compute the divisors of 1714?

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 1714 by each of the numbers from 1 to 1714 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)

1714 / 1 = 1714 (the remainder is 0, so 1 is a divisor of 1714)
1714 / 2 = 857 (the remainder is 0, so 2 is a divisor of 1714)
1714 / 3 = 571.33333333333 (the remainder is 1, so 3 is not a divisor of 1714)
...
1714 / 1713 = 1.0005837711617 (the remainder is 1, so 1713 is not a divisor of 1714)
1714 / 1714 = 1 (the remainder is 0, so 1714 is a divisor of 1714)

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 1714 (i.e. 41.400483088969). 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 $\frac{N}{d} = D$ )

1714 / 1 = 1714 (the remainder is 0, so 1 and 1714 are divisors of 1714)
1714 / 2 = 857 (the remainder is 0, so 2 and 857 are divisors of 1714)
1714 / 3 = 571.33333333333 (the remainder is 1, so 3 is not a divisor of 1714)
...
1714 / 40 = 42.85 (the remainder is 34, so 40 is not a divisor of 1714)
1714 / 41 = 41.80487804878 (the remainder is 33, so 41 is not a divisor of 1714)