What are the divisors of 1207?

1, 17, 71, 1207

There is a total of 4 positive divisors.
The sum of these divisors is 1296.
The arithmetic mean is 324.

4 odd divisors

1, 17, 71, 1207

How to compute the divisors of 1207?

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 1207 by each of the numbers from 1 to 1207 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)

1207 / 1 = 1207 (the remainder is 0, so 1 is a divisor of 1207)
1207 / 2 = 603.5 (the remainder is 1, so 2 is not a divisor of 1207)
1207 / 3 = 402.33333333333 (the remainder is 1, so 3 is not a divisor of 1207)
...
1207 / 1206 = 1.0008291873964 (the remainder is 1, so 1206 is not a divisor of 1207)
1207 / 1207 = 1 (the remainder is 0, so 1207 is a divisor of 1207)

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 1207 (i.e. 34.74190553208). 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 $\frac{N}{d} = D$ )

1207 / 1 = 1207 (the remainder is 0, so 1 and 1207 are divisors of 1207)
1207 / 2 = 603.5 (the remainder is 1, so 2 is not a divisor of 1207)
1207 / 3 = 402.33333333333 (the remainder is 1, so 3 is not a divisor of 1207)
...
1207 / 33 = 36.575757575758 (the remainder is 19, so 33 is not a divisor of 1207)
1207 / 34 = 35.5 (the remainder is 17, so 34 is not a divisor of 1207)