What are the divisors of 4929?

1, 3, 31, 53, 93, 159, 1643, 4929

There is a total of 8 positive divisors.
The sum of these divisors is 6912.
The arithmetic mean is 864.

8 odd divisors

1, 3, 31, 53, 93, 159, 1643, 4929

How to compute the divisors of 4929?

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 4929 by each of the numbers from 1 to 4929 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)

4929 / 1 = 4929 (the remainder is 0, so 1 is a divisor of 4929)
4929 / 2 = 2464.5 (the remainder is 1, so 2 is not a divisor of 4929)
4929 / 3 = 1643 (the remainder is 0, so 3 is a divisor of 4929)
...
4929 / 4928 = 1.0002029220779 (the remainder is 1, so 4928 is not a divisor of 4929)
4929 / 4929 = 1 (the remainder is 0, so 4929 is a divisor of 4929)

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 4929 (i.e. 70.206837273872). 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 $\frac{N}{d} = D$ )

4929 / 1 = 4929 (the remainder is 0, so 1 and 4929 are divisors of 4929)
4929 / 2 = 2464.5 (the remainder is 1, so 2 is not a divisor of 4929)
4929 / 3 = 1643 (the remainder is 0, so 3 and 1643 are divisors of 4929)
...
4929 / 69 = 71.434782608696 (the remainder is 30, so 69 is not a divisor of 4929)
4929 / 70 = 70.414285714286 (the remainder is 29, so 70 is not a divisor of 4929)