What are the divisors of 248?

1, 2, 4, 8, 31, 62, 124, 248

There is a total of 8 positive divisors.
The sum of these divisors is 480.
The arithmetic mean is 60.

6 even divisors

2, 4, 8, 62, 124, 248

2 odd divisors

1, 31

How to compute the divisors of 248?

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 248 by each of the numbers from 1 to 248 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)

248 / 1 = 248 (the remainder is 0, so 1 is a divisor of 248)
248 / 2 = 124 (the remainder is 0, so 2 is a divisor of 248)
248 / 3 = 82.666666666667 (the remainder is 2, so 3 is not a divisor of 248)
...
248 / 247 = 1.004048582996 (the remainder is 1, so 247 is not a divisor of 248)
248 / 248 = 1 (the remainder is 0, so 248 is a divisor of 248)

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 248 (i.e. 15.748015748024). 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 $\frac{N}{d} = D$ )

248 / 1 = 248 (the remainder is 0, so 1 and 248 are divisors of 248)
248 / 2 = 124 (the remainder is 0, so 2 and 124 are divisors of 248)
248 / 3 = 82.666666666667 (the remainder is 2, so 3 is not a divisor of 248)
...
248 / 14 = 17.714285714286 (the remainder is 10, so 14 is not a divisor of 248)
248 / 15 = 16.533333333333 (the remainder is 8, so 15 is not a divisor of 248)