What are the divisors of 4247?

1, 31, 137, 4247

There is a total of 4 positive divisors.
The sum of these divisors is 4416.
The arithmetic mean is 1104.

4 odd divisors

1, 31, 137, 4247

How to compute the divisors of 4247?

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 4247 by each of the numbers from 1 to 4247 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)

4247 / 1 = 4247 (the remainder is 0, so 1 is a divisor of 4247)
4247 / 2 = 2123.5 (the remainder is 1, so 2 is not a divisor of 4247)
4247 / 3 = 1415.6666666667 (the remainder is 2, so 3 is not a divisor of 4247)
...
4247 / 4246 = 1.0002355157796 (the remainder is 1, so 4246 is not a divisor of 4247)
4247 / 4247 = 1 (the remainder is 0, so 4247 is a divisor of 4247)

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 4247 (i.e. 65.169011040524). 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 $\frac{N}{d} = D$ )

4247 / 1 = 4247 (the remainder is 0, so 1 and 4247 are divisors of 4247)
4247 / 2 = 2123.5 (the remainder is 1, so 2 is not a divisor of 4247)
4247 / 3 = 1415.6666666667 (the remainder is 2, so 3 is not a divisor of 4247)
...
4247 / 64 = 66.359375 (the remainder is 23, so 64 is not a divisor of 4247)
4247 / 65 = 65.338461538462 (the remainder is 22, so 65 is not a divisor of 4247)