What are the divisors of 4954?

1, 2, 2477, 4954

There is a total of 4 positive divisors.
The sum of these divisors is 7434.
The arithmetic mean is 1858.5.

2 even divisors

2, 4954

2 odd divisors

1, 2477

How to compute the divisors of 4954?

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 4954 by each of the numbers from 1 to 4954 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)

4954 / 1 = 4954 (the remainder is 0, so 1 is a divisor of 4954)
4954 / 2 = 2477 (the remainder is 0, so 2 is a divisor of 4954)
4954 / 3 = 1651.3333333333 (the remainder is 1, so 3 is not a divisor of 4954)
...
4954 / 4953 = 1.0002018978397 (the remainder is 1, so 4953 is not a divisor of 4954)
4954 / 4954 = 1 (the remainder is 0, so 4954 is a divisor of 4954)

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 4954 (i.e. 70.384657419071). 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 $\frac{N}{d} = D$ )

4954 / 1 = 4954 (the remainder is 0, so 1 and 4954 are divisors of 4954)
4954 / 2 = 2477 (the remainder is 0, so 2 and 2477 are divisors of 4954)
4954 / 3 = 1651.3333333333 (the remainder is 1, so 3 is not a divisor of 4954)
...
4954 / 69 = 71.797101449275 (the remainder is 55, so 69 is not a divisor of 4954)
4954 / 70 = 70.771428571429 (the remainder is 54, so 70 is not a divisor of 4954)