What are the divisors of 4907?

1, 7, 701, 4907

There is a total of 4 positive divisors.
The sum of these divisors is 5616.
The arithmetic mean is 1404.

4 odd divisors

1, 7, 701, 4907

How to compute the divisors of 4907?

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 4907 by each of the numbers from 1 to 4907 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)

4907 / 1 = 4907 (the remainder is 0, so 1 is a divisor of 4907)
4907 / 2 = 2453.5 (the remainder is 1, so 2 is not a divisor of 4907)
4907 / 3 = 1635.6666666667 (the remainder is 2, so 3 is not a divisor of 4907)
...
4907 / 4906 = 1.0002038320424 (the remainder is 1, so 4906 is not a divisor of 4907)
4907 / 4907 = 1 (the remainder is 0, so 4907 is a divisor of 4907)

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 4907 (i.e. 70.049982155601). 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 $\frac{N}{d} = D$ )

4907 / 1 = 4907 (the remainder is 0, so 1 and 4907 are divisors of 4907)
4907 / 2 = 2453.5 (the remainder is 1, so 2 is not a divisor of 4907)
4907 / 3 = 1635.6666666667 (the remainder is 2, so 3 is not a divisor of 4907)
...
4907 / 69 = 71.115942028986 (the remainder is 8, so 69 is not a divisor of 4907)
4907 / 70 = 70.1 (the remainder is 7, so 70 is not a divisor of 4907)