What are the divisors of 4777?

1, 17, 281, 4777

There is a total of 4 positive divisors.
The sum of these divisors is 5076.
The arithmetic mean is 1269.

4 odd divisors

1, 17, 281, 4777

How to compute the divisors of 4777?

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 4777 by each of the numbers from 1 to 4777 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)

4777 / 1 = 4777 (the remainder is 0, so 1 is a divisor of 4777)
4777 / 2 = 2388.5 (the remainder is 1, so 2 is not a divisor of 4777)
4777 / 3 = 1592.3333333333 (the remainder is 1, so 3 is not a divisor of 4777)
...
4777 / 4776 = 1.0002093802345 (the remainder is 1, so 4776 is not a divisor of 4777)
4777 / 4777 = 1 (the remainder is 0, so 4777 is a divisor of 4777)

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 4777 (i.e. 69.11584478251). 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 $\frac{N}{d} = D$ )

4777 / 1 = 4777 (the remainder is 0, so 1 and 4777 are divisors of 4777)
4777 / 2 = 2388.5 (the remainder is 1, so 2 is not a divisor of 4777)
4777 / 3 = 1592.3333333333 (the remainder is 1, so 3 is not a divisor of 4777)
...
4777 / 68 = 70.25 (the remainder is 17, so 68 is not a divisor of 4777)
4777 / 69 = 69.231884057971 (the remainder is 16, so 69 is not a divisor of 4777)