What are the divisors of 4946?

1, 2, 2473, 4946

There is a total of 4 positive divisors.
The sum of these divisors is 7422.
The arithmetic mean is 1855.5.

2 even divisors

2, 4946

2 odd divisors

1, 2473

How to compute the divisors of 4946?

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 4946 by each of the numbers from 1 to 4946 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)

4946 / 1 = 4946 (the remainder is 0, so 1 is a divisor of 4946)
4946 / 2 = 2473 (the remainder is 0, so 2 is a divisor of 4946)
4946 / 3 = 1648.6666666667 (the remainder is 2, so 3 is not a divisor of 4946)
...
4946 / 4945 = 1.0002022244692 (the remainder is 1, so 4945 is not a divisor of 4946)
4946 / 4946 = 1 (the remainder is 0, so 4946 is a divisor of 4946)

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 4946 (i.e. 70.327803890069). 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 $\frac{N}{d} = D$ )

4946 / 1 = 4946 (the remainder is 0, so 1 and 4946 are divisors of 4946)
4946 / 2 = 2473 (the remainder is 0, so 2 and 2473 are divisors of 4946)
4946 / 3 = 1648.6666666667 (the remainder is 2, so 3 is not a divisor of 4946)
...
4946 / 69 = 71.68115942029 (the remainder is 47, so 69 is not a divisor of 4946)
4946 / 70 = 70.657142857143 (the remainder is 46, so 70 is not a divisor of 4946)