What are the divisors of 4892?

1, 2, 4, 1223, 2446, 4892

There is a total of 6 positive divisors.
The sum of these divisors is 8568.
The arithmetic mean is 1428.

4 even divisors

2, 4, 2446, 4892

2 odd divisors

1, 1223

How to compute the divisors of 4892?

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 4892 by each of the numbers from 1 to 4892 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)

4892 / 1 = 4892 (the remainder is 0, so 1 is a divisor of 4892)
4892 / 2 = 2446 (the remainder is 0, so 2 is a divisor of 4892)
4892 / 3 = 1630.6666666667 (the remainder is 2, so 3 is not a divisor of 4892)
...
4892 / 4891 = 1.0002044571662 (the remainder is 1, so 4891 is not a divisor of 4892)
4892 / 4892 = 1 (the remainder is 0, so 4892 is a divisor of 4892)

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 4892 (i.e. 69.942833800183). 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 $\frac{N}{d} = D$ )

4892 / 1 = 4892 (the remainder is 0, so 1 and 4892 are divisors of 4892)
4892 / 2 = 2446 (the remainder is 0, so 2 and 2446 are divisors of 4892)
4892 / 3 = 1630.6666666667 (the remainder is 2, so 3 is not a divisor of 4892)
...
4892 / 68 = 71.941176470588 (the remainder is 64, so 68 is not a divisor of 4892)
4892 / 69 = 70.898550724638 (the remainder is 62, so 69 is not a divisor of 4892)