What are the divisors of 2291?

1, 29, 79, 2291

There is a total of 4 positive divisors.
The sum of these divisors is 2400.
The arithmetic mean is 600.

4 odd divisors

1, 29, 79, 2291

How to compute the divisors of 2291?

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 2291 by each of the numbers from 1 to 2291 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)

2291 / 1 = 2291 (the remainder is 0, so 1 is a divisor of 2291)
2291 / 2 = 1145.5 (the remainder is 1, so 2 is not a divisor of 2291)
2291 / 3 = 763.66666666667 (the remainder is 2, so 3 is not a divisor of 2291)
...
2291 / 2290 = 1.0004366812227 (the remainder is 1, so 2290 is not a divisor of 2291)
2291 / 2291 = 1 (the remainder is 0, so 2291 is a divisor of 2291)

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 2291 (i.e. 47.864391775097). 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 $\frac{N}{d} = D$ )

2291 / 1 = 2291 (the remainder is 0, so 1 and 2291 are divisors of 2291)
2291 / 2 = 1145.5 (the remainder is 1, so 2 is not a divisor of 2291)
2291 / 3 = 763.66666666667 (the remainder is 2, so 3 is not a divisor of 2291)
...
2291 / 46 = 49.804347826087 (the remainder is 37, so 46 is not a divisor of 2291)
2291 / 47 = 48.744680851064 (the remainder is 35, so 47 is not a divisor of 2291)