What are the divisors of 280?

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280

There is a total of 16 positive divisors.
The sum of these divisors is 720.
The arithmetic mean is 45.

12 even divisors

2, 4, 8, 10, 14, 20, 28, 40, 56, 70, 140, 280

4 odd divisors

1, 5, 7, 35

How to compute the divisors of 280?

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 280 by each of the numbers from 1 to 280 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)

280 / 1 = 280 (the remainder is 0, so 1 is a divisor of 280)
280 / 2 = 140 (the remainder is 0, so 2 is a divisor of 280)
280 / 3 = 93.333333333333 (the remainder is 1, so 3 is not a divisor of 280)
...
280 / 279 = 1.0035842293907 (the remainder is 1, so 279 is not a divisor of 280)
280 / 280 = 1 (the remainder is 0, so 280 is a divisor of 280)

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 280 (i.e. 16.733200530682). 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 $\frac{N}{d} = D$ )

280 / 1 = 280 (the remainder is 0, so 1 and 280 are divisors of 280)
280 / 2 = 140 (the remainder is 0, so 2 and 140 are divisors of 280)
280 / 3 = 93.333333333333 (the remainder is 1, so 3 is not a divisor of 280)
...
280 / 15 = 18.666666666667 (the remainder is 10, so 15 is not a divisor of 280)
280 / 16 = 17.5 (the remainder is 8, so 16 is not a divisor of 280)