What are the divisors of 1671?

1, 3, 557, 1671

There is a total of 4 positive divisors.
The sum of these divisors is 2232.
The arithmetic mean is 558.

4 odd divisors

1, 3, 557, 1671

How to compute the divisors of 1671?

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 1671 by each of the numbers from 1 to 1671 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)

1671 / 1 = 1671 (the remainder is 0, so 1 is a divisor of 1671)
1671 / 2 = 835.5 (the remainder is 1, so 2 is not a divisor of 1671)
1671 / 3 = 557 (the remainder is 0, so 3 is a divisor of 1671)
...
1671 / 1670 = 1.0005988023952 (the remainder is 1, so 1670 is not a divisor of 1671)
1671 / 1671 = 1 (the remainder is 0, so 1671 is a divisor of 1671)

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 1671 (i.e. 40.877866871939). 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 $\frac{N}{d} = D$ )

1671 / 1 = 1671 (the remainder is 0, so 1 and 1671 are divisors of 1671)
1671 / 2 = 835.5 (the remainder is 1, so 2 is not a divisor of 1671)
1671 / 3 = 557 (the remainder is 0, so 3 and 557 are divisors of 1671)
...
1671 / 39 = 42.846153846154 (the remainder is 33, so 39 is not a divisor of 1671)
1671 / 40 = 41.775 (the remainder is 31, so 40 is not a divisor of 1671)