What are the divisors of 4494?

1, 2, 3, 6, 7, 14, 21, 42, 107, 214, 321, 642, 749, 1498, 2247, 4494

There is a total of 16 positive divisors.
The sum of these divisors is 10368.
The arithmetic mean is 648.

8 even divisors

2, 6, 14, 42, 214, 642, 1498, 4494

8 odd divisors

1, 3, 7, 21, 107, 321, 749, 2247

How to compute the divisors of 4494?

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 4494 by each of the numbers from 1 to 4494 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)

4494 / 1 = 4494 (the remainder is 0, so 1 is a divisor of 4494)
4494 / 2 = 2247 (the remainder is 0, so 2 is a divisor of 4494)
4494 / 3 = 1498 (the remainder is 0, so 3 is a divisor of 4494)
...
4494 / 4493 = 1.0002225684398 (the remainder is 1, so 4493 is not a divisor of 4494)
4494 / 4494 = 1 (the remainder is 0, so 4494 is a divisor of 4494)

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 4494 (i.e. 67.037303048377). 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 $\frac{N}{d} = D$ )

4494 / 1 = 4494 (the remainder is 0, so 1 and 4494 are divisors of 4494)
4494 / 2 = 2247 (the remainder is 0, so 2 and 2247 are divisors of 4494)
4494 / 3 = 1498 (the remainder is 0, so 3 and 1498 are divisors of 4494)
...
4494 / 66 = 68.090909090909 (the remainder is 6, so 66 is not a divisor of 4494)
4494 / 67 = 67.074626865672 (the remainder is 5, so 67 is not a divisor of 4494)