What are the divisors of 277?

1, 277

There is a total of 2 positive divisors.
The sum of these divisors is 278.
The arithmetic mean is 139.

2 odd divisors

1, 277

How to compute the divisors of 277?

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 277 by each of the numbers from 1 to 277 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)

277 / 1 = 277 (the remainder is 0, so 1 is a divisor of 277)
277 / 2 = 138.5 (the remainder is 1, so 2 is not a divisor of 277)
277 / 3 = 92.333333333333 (the remainder is 1, so 3 is not a divisor of 277)
...
277 / 276 = 1.0036231884058 (the remainder is 1, so 276 is not a divisor of 277)
277 / 277 = 1 (the remainder is 0, so 277 is a divisor of 277)

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 277 (i.e. 16.643316977093). 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 $\frac{N}{d} = D$ )

277 / 1 = 277 (the remainder is 0, so 1 and 277 are divisors of 277)
277 / 2 = 138.5 (the remainder is 1, so 2 is not a divisor of 277)
277 / 3 = 92.333333333333 (the remainder is 1, so 3 is not a divisor of 277)
...
277 / 15 = 18.466666666667 (the remainder is 7, so 15 is not a divisor of 277)
277 / 16 = 17.3125 (the remainder is 5, so 16 is not a divisor of 277)