What are the divisors of 276?

1, 2, 3, 4, 6, 12, 23, 46, 69, 92, 138, 276

There is a total of 12 positive divisors.
The sum of these divisors is 672.
The arithmetic mean is 56.

8 even divisors

2, 4, 6, 12, 46, 92, 138, 276

4 odd divisors

1, 3, 23, 69

How to compute the divisors of 276?

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 276 by each of the numbers from 1 to 276 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)

276 / 1 = 276 (the remainder is 0, so 1 is a divisor of 276)
276 / 2 = 138 (the remainder is 0, so 2 is a divisor of 276)
276 / 3 = 92 (the remainder is 0, so 3 is a divisor of 276)
...
276 / 275 = 1.0036363636364 (the remainder is 1, so 275 is not a divisor of 276)
276 / 276 = 1 (the remainder is 0, so 276 is a divisor of 276)

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 276 (i.e. 16.613247725836). 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 $\frac{N}{d} = D$ )

276 / 1 = 276 (the remainder is 0, so 1 and 276 are divisors of 276)
276 / 2 = 138 (the remainder is 0, so 2 and 138 are divisors of 276)
276 / 3 = 92 (the remainder is 0, so 3 and 92 are divisors of 276)
...
276 / 15 = 18.4 (the remainder is 6, so 15 is not a divisor of 276)
276 / 16 = 17.25 (the remainder is 4, so 16 is not a divisor of 276)