What are the divisors of 2147?

1, 19, 113, 2147

There is a total of 4 positive divisors.
The sum of these divisors is 2280.
The arithmetic mean is 570.

4 odd divisors

1, 19, 113, 2147

How to compute the divisors of 2147?

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 2147 by each of the numbers from 1 to 2147 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)

2147 / 1 = 2147 (the remainder is 0, so 1 is a divisor of 2147)
2147 / 2 = 1073.5 (the remainder is 1, so 2 is not a divisor of 2147)
2147 / 3 = 715.66666666667 (the remainder is 2, so 3 is not a divisor of 2147)
...
2147 / 2146 = 1.0004659832246 (the remainder is 1, so 2146 is not a divisor of 2147)
2147 / 2147 = 1 (the remainder is 0, so 2147 is a divisor of 2147)

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 2147 (i.e. 46.335731352812). 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 $\frac{N}{d} = D$ )

2147 / 1 = 2147 (the remainder is 0, so 1 and 2147 are divisors of 2147)
2147 / 2 = 1073.5 (the remainder is 1, so 2 is not a divisor of 2147)
2147 / 3 = 715.66666666667 (the remainder is 2, so 3 is not a divisor of 2147)
...
2147 / 45 = 47.711111111111 (the remainder is 32, so 45 is not a divisor of 2147)
2147 / 46 = 46.673913043478 (the remainder is 31, so 46 is not a divisor of 2147)