What are the divisors of 4607?

1, 17, 271, 4607

There is a total of 4 positive divisors.
The sum of these divisors is 4896.
The arithmetic mean is 1224.

4 odd divisors

1, 17, 271, 4607

How to compute the divisors of 4607?

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 4607 by each of the numbers from 1 to 4607 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)

4607 / 1 = 4607 (the remainder is 0, so 1 is a divisor of 4607)
4607 / 2 = 2303.5 (the remainder is 1, so 2 is not a divisor of 4607)
4607 / 3 = 1535.6666666667 (the remainder is 2, so 3 is not a divisor of 4607)
...
4607 / 4606 = 1.0002171081198 (the remainder is 1, so 4606 is not a divisor of 4607)
4607 / 4607 = 1 (the remainder is 0, so 4607 is a divisor of 4607)

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 4607 (i.e. 67.874884898613). 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 $\frac{N}{d} = D$ )

4607 / 1 = 4607 (the remainder is 0, so 1 and 4607 are divisors of 4607)
4607 / 2 = 2303.5 (the remainder is 1, so 2 is not a divisor of 4607)
4607 / 3 = 1535.6666666667 (the remainder is 2, so 3 is not a divisor of 4607)
...
4607 / 66 = 69.80303030303 (the remainder is 53, so 66 is not a divisor of 4607)
4607 / 67 = 68.761194029851 (the remainder is 51, so 67 is not a divisor of 4607)