What are the divisors of 4957?

1, 4957

There is a total of 2 positive divisors.
The sum of these divisors is 4958.
The arithmetic mean is 2479.

2 odd divisors

1, 4957

How to compute the divisors of 4957?

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 4957 by each of the numbers from 1 to 4957 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)

4957 / 1 = 4957 (the remainder is 0, so 1 is a divisor of 4957)
4957 / 2 = 2478.5 (the remainder is 1, so 2 is not a divisor of 4957)
4957 / 3 = 1652.3333333333 (the remainder is 1, so 3 is not a divisor of 4957)
...
4957 / 4956 = 1.0002017756255 (the remainder is 1, so 4956 is not a divisor of 4957)
4957 / 4957 = 1 (the remainder is 0, so 4957 is a divisor of 4957)

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 4957 (i.e. 70.405965656328). 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 $\frac{N}{d} = D$ )

4957 / 1 = 4957 (the remainder is 0, so 1 and 4957 are divisors of 4957)
4957 / 2 = 2478.5 (the remainder is 1, so 2 is not a divisor of 4957)
4957 / 3 = 1652.3333333333 (the remainder is 1, so 3 is not a divisor of 4957)
...
4957 / 69 = 71.840579710145 (the remainder is 58, so 69 is not a divisor of 4957)
4957 / 70 = 70.814285714286 (the remainder is 57, so 70 is not a divisor of 4957)