What are the divisors of 4963?

1, 7, 709, 4963

There is a total of 4 positive divisors.
The sum of these divisors is 5680.
The arithmetic mean is 1420.

4 odd divisors

1, 7, 709, 4963

How to compute the divisors of 4963?

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 4963 by each of the numbers from 1 to 4963 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)

4963 / 1 = 4963 (the remainder is 0, so 1 is a divisor of 4963)
4963 / 2 = 2481.5 (the remainder is 1, so 2 is not a divisor of 4963)
4963 / 3 = 1654.3333333333 (the remainder is 1, so 3 is not a divisor of 4963)
...
4963 / 4962 = 1.0002015316405 (the remainder is 1, so 4962 is not a divisor of 4963)
4963 / 4963 = 1 (the remainder is 0, so 4963 is a divisor of 4963)

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 4963 (i.e. 70.448562795844). 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 $\frac{N}{d} = D$ )

4963 / 1 = 4963 (the remainder is 0, so 1 and 4963 are divisors of 4963)
4963 / 2 = 2481.5 (the remainder is 1, so 2 is not a divisor of 4963)
4963 / 3 = 1654.3333333333 (the remainder is 1, so 3 is not a divisor of 4963)
...
4963 / 69 = 71.927536231884 (the remainder is 64, so 69 is not a divisor of 4963)
4963 / 70 = 70.9 (the remainder is 63, so 70 is not a divisor of 4963)