What are the divisors of 2279?

1, 43, 53, 2279

There is a total of 4 positive divisors.
The sum of these divisors is 2376.
The arithmetic mean is 594.

4 odd divisors

1, 43, 53, 2279

How to compute the divisors of 2279?

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 2279 by each of the numbers from 1 to 2279 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)

2279 / 1 = 2279 (the remainder is 0, so 1 is a divisor of 2279)
2279 / 2 = 1139.5 (the remainder is 1, so 2 is not a divisor of 2279)
2279 / 3 = 759.66666666667 (the remainder is 2, so 3 is not a divisor of 2279)
...
2279 / 2278 = 1.0004389815628 (the remainder is 1, so 2278 is not a divisor of 2279)
2279 / 2279 = 1 (the remainder is 0, so 2279 is a divisor of 2279)

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 2279 (i.e. 47.73887304912). 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 $\frac{N}{d} = D$ )

2279 / 1 = 2279 (the remainder is 0, so 1 and 2279 are divisors of 2279)
2279 / 2 = 1139.5 (the remainder is 1, so 2 is not a divisor of 2279)
2279 / 3 = 759.66666666667 (the remainder is 2, so 3 is not a divisor of 2279)
...
2279 / 46 = 49.54347826087 (the remainder is 25, so 46 is not a divisor of 2279)
2279 / 47 = 48.489361702128 (the remainder is 23, so 47 is not a divisor of 2279)