What are the divisors of 4937?

1, 4937

There is a total of 2 positive divisors.
The sum of these divisors is 4938.
The arithmetic mean is 2469.

2 odd divisors

1, 4937

How to compute the divisors of 4937?

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 4937 by each of the numbers from 1 to 4937 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)

4937 / 1 = 4937 (the remainder is 0, so 1 is a divisor of 4937)
4937 / 2 = 2468.5 (the remainder is 1, so 2 is not a divisor of 4937)
4937 / 3 = 1645.6666666667 (the remainder is 2, so 3 is not a divisor of 4937)
...
4937 / 4936 = 1.0002025931929 (the remainder is 1, so 4936 is not a divisor of 4937)
4937 / 4937 = 1 (the remainder is 0, so 4937 is a divisor of 4937)

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 4937 (i.e. 70.263788682365). 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 $\frac{N}{d} = D$ )

4937 / 1 = 4937 (the remainder is 0, so 1 and 4937 are divisors of 4937)
4937 / 2 = 2468.5 (the remainder is 1, so 2 is not a divisor of 4937)
4937 / 3 = 1645.6666666667 (the remainder is 2, so 3 is not a divisor of 4937)
...
4937 / 69 = 71.550724637681 (the remainder is 38, so 69 is not a divisor of 4937)
4937 / 70 = 70.528571428571 (the remainder is 37, so 70 is not a divisor of 4937)