What are the divisors of 247?

1, 13, 19, 247

There is a total of 4 positive divisors.
The sum of these divisors is 280.
The arithmetic mean is 70.

4 odd divisors

1, 13, 19, 247

How to compute the divisors of 247?

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 247 by each of the numbers from 1 to 247 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)

247 / 1 = 247 (the remainder is 0, so 1 is a divisor of 247)
247 / 2 = 123.5 (the remainder is 1, so 2 is not a divisor of 247)
247 / 3 = 82.333333333333 (the remainder is 1, so 3 is not a divisor of 247)
...
247 / 246 = 1.0040650406504 (the remainder is 1, so 246 is not a divisor of 247)
247 / 247 = 1 (the remainder is 0, so 247 is a divisor of 247)

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 247 (i.e. 15.716233645502). 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 $\frac{N}{d} = D$ )

247 / 1 = 247 (the remainder is 0, so 1 and 247 are divisors of 247)
247 / 2 = 123.5 (the remainder is 1, so 2 is not a divisor of 247)
247 / 3 = 82.333333333333 (the remainder is 1, so 3 is not a divisor of 247)
...
247 / 14 = 17.642857142857 (the remainder is 9, so 14 is not a divisor of 247)
247 / 15 = 16.466666666667 (the remainder is 7, so 15 is not a divisor of 247)