What are the divisors of 4277?

1, 7, 13, 47, 91, 329, 611, 4277

There is a total of 8 positive divisors.
The sum of these divisors is 5376.
The arithmetic mean is 672.

8 odd divisors

1, 7, 13, 47, 91, 329, 611, 4277

How to compute the divisors of 4277?

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 4277 by each of the numbers from 1 to 4277 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)

4277 / 1 = 4277 (the remainder is 0, so 1 is a divisor of 4277)
4277 / 2 = 2138.5 (the remainder is 1, so 2 is not a divisor of 4277)
4277 / 3 = 1425.6666666667 (the remainder is 2, so 3 is not a divisor of 4277)
...
4277 / 4276 = 1.0002338634238 (the remainder is 1, so 4276 is not a divisor of 4277)
4277 / 4277 = 1 (the remainder is 0, so 4277 is a divisor of 4277)

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 4277 (i.e. 65.39877674697). 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 $\frac{N}{d} = D$ )

4277 / 1 = 4277 (the remainder is 0, so 1 and 4277 are divisors of 4277)
4277 / 2 = 2138.5 (the remainder is 1, so 2 is not a divisor of 4277)
4277 / 3 = 1425.6666666667 (the remainder is 2, so 3 is not a divisor of 4277)
...
4277 / 64 = 66.828125 (the remainder is 53, so 64 is not a divisor of 4277)
4277 / 65 = 65.8 (the remainder is 52, so 65 is not a divisor of 4277)