What are the divisors of 4891?

1, 67, 73, 4891

There is a total of 4 positive divisors.
The sum of these divisors is 5032.
The arithmetic mean is 1258.

4 odd divisors

1, 67, 73, 4891

How to compute the divisors of 4891?

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 4891 by each of the numbers from 1 to 4891 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)

4891 / 1 = 4891 (the remainder is 0, so 1 is a divisor of 4891)
4891 / 2 = 2445.5 (the remainder is 1, so 2 is not a divisor of 4891)
4891 / 3 = 1630.3333333333 (the remainder is 1, so 3 is not a divisor of 4891)
...
4891 / 4890 = 1.0002044989775 (the remainder is 1, so 4890 is not a divisor of 4891)
4891 / 4891 = 1 (the remainder is 0, so 4891 is a divisor of 4891)

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 4891 (i.e. 69.935684739623). 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 $\frac{N}{d} = D$ )

4891 / 1 = 4891 (the remainder is 0, so 1 and 4891 are divisors of 4891)
4891 / 2 = 2445.5 (the remainder is 1, so 2 is not a divisor of 4891)
4891 / 3 = 1630.3333333333 (the remainder is 1, so 3 is not a divisor of 4891)
...
4891 / 68 = 71.926470588235 (the remainder is 63, so 68 is not a divisor of 4891)
4891 / 69 = 70.884057971014 (the remainder is 61, so 69 is not a divisor of 4891)