What are the divisors of 4914?

1, 2, 3, 6, 7, 9, 13, 14, 18, 21, 26, 27, 39, 42, 54, 63, 78, 91, 117, 126, 182, 189, 234, 273, 351, 378, 546, 702, 819, 1638, 2457, 4914

There is a total of 32 positive divisors.
The sum of these divisors is 13440.
The arithmetic mean is 420.

16 even divisors

2, 6, 14, 18, 26, 42, 54, 78, 126, 182, 234, 378, 546, 702, 1638, 4914

16 odd divisors

1, 3, 7, 9, 13, 21, 27, 39, 63, 91, 117, 189, 273, 351, 819, 2457

How to compute the divisors of 4914?

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 4914 by each of the numbers from 1 to 4914 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)

4914 / 1 = 4914 (the remainder is 0, so 1 is a divisor of 4914)
4914 / 2 = 2457 (the remainder is 0, so 2 is a divisor of 4914)
4914 / 3 = 1638 (the remainder is 0, so 3 is a divisor of 4914)
...
4914 / 4913 = 1.0002035416243 (the remainder is 1, so 4913 is not a divisor of 4914)
4914 / 4914 = 1 (the remainder is 0, so 4914 is a divisor of 4914)

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 4914 (i.e. 70.099928673288). 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 $\frac{N}{d} = D$ )

4914 / 1 = 4914 (the remainder is 0, so 1 and 4914 are divisors of 4914)
4914 / 2 = 2457 (the remainder is 0, so 2 and 2457 are divisors of 4914)
4914 / 3 = 1638 (the remainder is 0, so 3 and 1638 are divisors of 4914)
...
4914 / 69 = 71.217391304348 (the remainder is 15, so 69 is not a divisor of 4914)
4914 / 70 = 70.2 (the remainder is 14, so 70 is not a divisor of 4914)