What are the divisors of 4774?

1, 2, 7, 11, 14, 22, 31, 62, 77, 154, 217, 341, 434, 682, 2387, 4774

There is a total of 16 positive divisors.
The sum of these divisors is 9216.
The arithmetic mean is 576.

8 even divisors

2, 14, 22, 62, 154, 434, 682, 4774

8 odd divisors

1, 7, 11, 31, 77, 217, 341, 2387

How to compute the divisors of 4774?

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 4774 by each of the numbers from 1 to 4774 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)

4774 / 1 = 4774 (the remainder is 0, so 1 is a divisor of 4774)
4774 / 2 = 2387 (the remainder is 0, so 2 is a divisor of 4774)
4774 / 3 = 1591.3333333333 (the remainder is 1, so 3 is not a divisor of 4774)
...
4774 / 4773 = 1.0002095118374 (the remainder is 1, so 4773 is not a divisor of 4774)
4774 / 4774 = 1 (the remainder is 0, so 4774 is a divisor of 4774)

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 4774 (i.e. 69.094138680499). 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 $\frac{N}{d} = D$ )

4774 / 1 = 4774 (the remainder is 0, so 1 and 4774 are divisors of 4774)
4774 / 2 = 2387 (the remainder is 0, so 2 and 2387 are divisors of 4774)
4774 / 3 = 1591.3333333333 (the remainder is 1, so 3 is not a divisor of 4774)
...
4774 / 68 = 70.205882352941 (the remainder is 14, so 68 is not a divisor of 4774)
4774 / 69 = 69.188405797101 (the remainder is 13, so 69 is not a divisor of 4774)