What are the divisors of 4278?

1, 2, 3, 6, 23, 31, 46, 62, 69, 93, 138, 186, 713, 1426, 2139, 4278

There is a total of 16 positive divisors.
The sum of these divisors is 9216.
The arithmetic mean is 576.

8 even divisors

2, 6, 46, 62, 138, 186, 1426, 4278

8 odd divisors

1, 3, 23, 31, 69, 93, 713, 2139

How to compute the divisors of 4278?

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 4278 by each of the numbers from 1 to 4278 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)

4278 / 1 = 4278 (the remainder is 0, so 1 is a divisor of 4278)
4278 / 2 = 2139 (the remainder is 0, so 2 is a divisor of 4278)
4278 / 3 = 1426 (the remainder is 0, so 3 is a divisor of 4278)
...
4278 / 4277 = 1.0002338087444 (the remainder is 1, so 4277 is not a divisor of 4278)
4278 / 4278 = 1 (the remainder is 0, so 4278 is a divisor of 4278)

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 4278 (i.e. 65.406421703071). 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 $\frac{N}{d} = D$ )

4278 / 1 = 4278 (the remainder is 0, so 1 and 4278 are divisors of 4278)
4278 / 2 = 2139 (the remainder is 0, so 2 and 2139 are divisors of 4278)
4278 / 3 = 1426 (the remainder is 0, so 3 and 1426 are divisors of 4278)
...
4278 / 64 = 66.84375 (the remainder is 54, so 64 is not a divisor of 4278)
4278 / 65 = 65.815384615385 (the remainder is 53, so 65 is not a divisor of 4278)