What are the divisors of 4757?

1, 67, 71, 4757

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

4 odd divisors

1, 67, 71, 4757

How to compute the divisors of 4757?

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 4757 by each of the numbers from 1 to 4757 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)

4757 / 1 = 4757 (the remainder is 0, so 1 is a divisor of 4757)
4757 / 2 = 2378.5 (the remainder is 1, so 2 is not a divisor of 4757)
4757 / 3 = 1585.6666666667 (the remainder is 2, so 3 is not a divisor of 4757)
...
4757 / 4756 = 1.0002102607233 (the remainder is 1, so 4756 is not a divisor of 4757)
4757 / 4757 = 1 (the remainder is 0, so 4757 is a divisor of 4757)

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 4757 (i.e. 68.971008402082). 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 $\frac{N}{d} = D$ )

4757 / 1 = 4757 (the remainder is 0, so 1 and 4757 are divisors of 4757)
4757 / 2 = 2378.5 (the remainder is 1, so 2 is not a divisor of 4757)
4757 / 3 = 1585.6666666667 (the remainder is 2, so 3 is not a divisor of 4757)
...
4757 / 67 = 71 (the remainder is 0, so 67 and 71 are divisors of 4757)
4757 / 68 = 69.955882352941 (the remainder is 65, so 68 is not a divisor of 4757)