What are the divisors of 1700?

1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, 850, 1700

There is a total of 18 positive divisors.
The sum of these divisors is 3906.
The arithmetic mean is 217.

12 even divisors

2, 4, 10, 20, 34, 50, 68, 100, 170, 340, 850, 1700

6 odd divisors

1, 5, 17, 25, 85, 425

How to compute the divisors of 1700?

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 1700 by each of the numbers from 1 to 1700 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)

1700 / 1 = 1700 (the remainder is 0, so 1 is a divisor of 1700)
1700 / 2 = 850 (the remainder is 0, so 2 is a divisor of 1700)
1700 / 3 = 566.66666666667 (the remainder is 2, so 3 is not a divisor of 1700)
...
1700 / 1699 = 1.0005885815185 (the remainder is 1, so 1699 is not a divisor of 1700)
1700 / 1700 = 1 (the remainder is 0, so 1700 is a divisor of 1700)

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 1700 (i.e. 41.231056256177). 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 $\frac{N}{d} = D$ )

1700 / 1 = 1700 (the remainder is 0, so 1 and 1700 are divisors of 1700)
1700 / 2 = 850 (the remainder is 0, so 2 and 850 are divisors of 1700)
1700 / 3 = 566.66666666667 (the remainder is 2, so 3 is not a divisor of 1700)
...
1700 / 40 = 42.5 (the remainder is 20, so 40 is not a divisor of 1700)
1700 / 41 = 41.463414634146 (the remainder is 19, so 41 is not a divisor of 1700)