What are the divisors of 4291?

1, 7, 613, 4291

There is a total of 4 positive divisors.
The sum of these divisors is 4912.
The arithmetic mean is 1228.

4 odd divisors

1, 7, 613, 4291

How to compute the divisors of 4291?

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 4291 by each of the numbers from 1 to 4291 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)

4291 / 1 = 4291 (the remainder is 0, so 1 is a divisor of 4291)
4291 / 2 = 2145.5 (the remainder is 1, so 2 is not a divisor of 4291)
4291 / 3 = 1430.3333333333 (the remainder is 1, so 3 is not a divisor of 4291)
...
4291 / 4290 = 1.0002331002331 (the remainder is 1, so 4290 is not a divisor of 4291)
4291 / 4291 = 1 (the remainder is 0, so 4291 is a divisor of 4291)

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 4291 (i.e. 65.505724940649). 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 $\frac{N}{d} = D$ )

4291 / 1 = 4291 (the remainder is 0, so 1 and 4291 are divisors of 4291)
4291 / 2 = 2145.5 (the remainder is 1, so 2 is not a divisor of 4291)
4291 / 3 = 1430.3333333333 (the remainder is 1, so 3 is not a divisor of 4291)
...
4291 / 64 = 67.046875 (the remainder is 3, so 64 is not a divisor of 4291)
4291 / 65 = 66.015384615385 (the remainder is 1, so 65 is not a divisor of 4291)