What are the divisors of 4958?

1, 2, 37, 67, 74, 134, 2479, 4958

There is a total of 8 positive divisors.
The sum of these divisors is 7752.
The arithmetic mean is 969.

4 even divisors

2, 74, 134, 4958

4 odd divisors

1, 37, 67, 2479

How to compute the divisors of 4958?

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 4958 by each of the numbers from 1 to 4958 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)

4958 / 1 = 4958 (the remainder is 0, so 1 is a divisor of 4958)
4958 / 2 = 2479 (the remainder is 0, so 2 is a divisor of 4958)
4958 / 3 = 1652.6666666667 (the remainder is 2, so 3 is not a divisor of 4958)
...
4958 / 4957 = 1.0002017349203 (the remainder is 1, so 4957 is not a divisor of 4958)
4958 / 4958 = 1 (the remainder is 0, so 4958 is a divisor of 4958)

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 4958 (i.e. 70.413066969136). 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 $\frac{N}{d} = D$ )

4958 / 1 = 4958 (the remainder is 0, so 1 and 4958 are divisors of 4958)
4958 / 2 = 2479 (the remainder is 0, so 2 and 2479 are divisors of 4958)
4958 / 3 = 1652.6666666667 (the remainder is 2, so 3 is not a divisor of 4958)
...
4958 / 69 = 71.855072463768 (the remainder is 59, so 69 is not a divisor of 4958)
4958 / 70 = 70.828571428571 (the remainder is 58, so 70 is not a divisor of 4958)