What are the divisors of 4953?

1, 3, 13, 39, 127, 381, 1651, 4953

There is a total of 8 positive divisors.
The sum of these divisors is 7168.
The arithmetic mean is 896.

8 odd divisors

1, 3, 13, 39, 127, 381, 1651, 4953

How to compute the divisors of 4953?

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 4953 by each of the numbers from 1 to 4953 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)

4953 / 1 = 4953 (the remainder is 0, so 1 is a divisor of 4953)
4953 / 2 = 2476.5 (the remainder is 1, so 2 is not a divisor of 4953)
4953 / 3 = 1651 (the remainder is 0, so 3 is a divisor of 4953)
...
4953 / 4952 = 1.0002019386107 (the remainder is 1, so 4952 is not a divisor of 4953)
4953 / 4953 = 1 (the remainder is 0, so 4953 is a divisor of 4953)

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 4953 (i.e. 70.377553239652). 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 $\frac{N}{d} = D$ )

4953 / 1 = 4953 (the remainder is 0, so 1 and 4953 are divisors of 4953)
4953 / 2 = 2476.5 (the remainder is 1, so 2 is not a divisor of 4953)
4953 / 3 = 1651 (the remainder is 0, so 3 and 1651 are divisors of 4953)
...
4953 / 69 = 71.782608695652 (the remainder is 54, so 69 is not a divisor of 4953)
4953 / 70 = 70.757142857143 (the remainder is 53, so 70 is not a divisor of 4953)