What are the divisors of 1670?

1, 2, 5, 10, 167, 334, 835, 1670

There is a total of 8 positive divisors.
The sum of these divisors is 3024.
The arithmetic mean is 378.

4 even divisors

2, 10, 334, 1670

4 odd divisors

1, 5, 167, 835

How to compute the divisors of 1670?

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 1670 by each of the numbers from 1 to 1670 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)

1670 / 1 = 1670 (the remainder is 0, so 1 is a divisor of 1670)
1670 / 2 = 835 (the remainder is 0, so 2 is a divisor of 1670)
1670 / 3 = 556.66666666667 (the remainder is 2, so 3 is not a divisor of 1670)
...
1670 / 1669 = 1.0005991611744 (the remainder is 1, so 1669 is not a divisor of 1670)
1670 / 1670 = 1 (the remainder is 0, so 1670 is a divisor of 1670)

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 1670 (i.e. 40.865633483405). 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 $\frac{N}{d} = D$ )

1670 / 1 = 1670 (the remainder is 0, so 1 and 1670 are divisors of 1670)
1670 / 2 = 835 (the remainder is 0, so 2 and 835 are divisors of 1670)
1670 / 3 = 556.66666666667 (the remainder is 2, so 3 is not a divisor of 1670)
...
1670 / 39 = 42.820512820513 (the remainder is 32, so 39 is not a divisor of 1670)
1670 / 40 = 41.75 (the remainder is 30, so 40 is not a divisor of 1670)