What are the divisors of 4294?

1, 2, 19, 38, 113, 226, 2147, 4294

There is a total of 8 positive divisors.
The sum of these divisors is 6840.
The arithmetic mean is 855.

4 even divisors

2, 38, 226, 4294

4 odd divisors

1, 19, 113, 2147

How to compute the divisors of 4294?

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 4294 by each of the numbers from 1 to 4294 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)

4294 / 1 = 4294 (the remainder is 0, so 1 is a divisor of 4294)
4294 / 2 = 2147 (the remainder is 0, so 2 is a divisor of 4294)
4294 / 3 = 1431.3333333333 (the remainder is 1, so 3 is not a divisor of 4294)
...
4294 / 4293 = 1.0002329373399 (the remainder is 1, so 4293 is not a divisor of 4294)
4294 / 4294 = 1 (the remainder is 0, so 4294 is a divisor of 4294)

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 4294 (i.e. 65.528619701623). 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 $\frac{N}{d} = D$ )

4294 / 1 = 4294 (the remainder is 0, so 1 and 4294 are divisors of 4294)
4294 / 2 = 2147 (the remainder is 0, so 2 and 2147 are divisors of 4294)
4294 / 3 = 1431.3333333333 (the remainder is 1, so 3 is not a divisor of 4294)
...
4294 / 64 = 67.09375 (the remainder is 6, so 64 is not a divisor of 4294)
4294 / 65 = 66.061538461538 (the remainder is 4, so 65 is not a divisor of 4294)