What are the divisors of 278?

1, 2, 139, 278

There is a total of 4 positive divisors.
The sum of these divisors is 420.
The arithmetic mean is 105.

2 even divisors

2, 278

2 odd divisors

1, 139

How to compute the divisors of 278?

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 278 by each of the numbers from 1 to 278 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)

278 / 1 = 278 (the remainder is 0, so 1 is a divisor of 278)
278 / 2 = 139 (the remainder is 0, so 2 is a divisor of 278)
278 / 3 = 92.666666666667 (the remainder is 2, so 3 is not a divisor of 278)
...
278 / 277 = 1.0036101083032 (the remainder is 1, so 277 is not a divisor of 278)
278 / 278 = 1 (the remainder is 0, so 278 is a divisor of 278)

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 278 (i.e. 16.673332000533). 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 $\frac{N}{d} = D$ )

278 / 1 = 278 (the remainder is 0, so 1 and 278 are divisors of 278)
278 / 2 = 139 (the remainder is 0, so 2 and 139 are divisors of 278)
278 / 3 = 92.666666666667 (the remainder is 2, so 3 is not a divisor of 278)
...
278 / 15 = 18.533333333333 (the remainder is 8, so 15 is not a divisor of 278)
278 / 16 = 17.375 (the remainder is 6, so 16 is not a divisor of 278)