What are the divisors of 1675?

1, 5, 25, 67, 335, 1675

There is a total of 6 positive divisors.
The sum of these divisors is 2108.
The arithmetic mean is 351.33333333333.

6 odd divisors

1, 5, 25, 67, 335, 1675

How to compute the divisors of 1675?

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 1675 by each of the numbers from 1 to 1675 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)

1675 / 1 = 1675 (the remainder is 0, so 1 is a divisor of 1675)
1675 / 2 = 837.5 (the remainder is 1, so 2 is not a divisor of 1675)
1675 / 3 = 558.33333333333 (the remainder is 1, so 3 is not a divisor of 1675)
...
1675 / 1674 = 1.0005973715651 (the remainder is 1, so 1674 is not a divisor of 1675)
1675 / 1675 = 1 (the remainder is 0, so 1675 is a divisor of 1675)

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 1675 (i.e. 40.926763859362). 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 $\frac{N}{d} = D$ )

1675 / 1 = 1675 (the remainder is 0, so 1 and 1675 are divisors of 1675)
1675 / 2 = 837.5 (the remainder is 1, so 2 is not a divisor of 1675)
1675 / 3 = 558.33333333333 (the remainder is 1, so 3 is not a divisor of 1675)
...
1675 / 39 = 42.948717948718 (the remainder is 37, so 39 is not a divisor of 1675)
1675 / 40 = 41.875 (the remainder is 35, so 40 is not a divisor of 1675)