What are the divisors of 4694?

1, 2, 2347, 4694

There is a total of 4 positive divisors.
The sum of these divisors is 7044.
The arithmetic mean is 1761.

2 even divisors

2, 4694

2 odd divisors

1, 2347

How to compute the divisors of 4694?

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 4694 by each of the numbers from 1 to 4694 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)

4694 / 1 = 4694 (the remainder is 0, so 1 is a divisor of 4694)
4694 / 2 = 2347 (the remainder is 0, so 2 is a divisor of 4694)
4694 / 3 = 1564.6666666667 (the remainder is 2, so 3 is not a divisor of 4694)
...
4694 / 4693 = 1.0002130833156 (the remainder is 1, so 4693 is not a divisor of 4694)
4694 / 4694 = 1 (the remainder is 0, so 4694 is a divisor of 4694)

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 4694 (i.e. 68.512772531843). 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 $\frac{N}{d} = D$ )

4694 / 1 = 4694 (the remainder is 0, so 1 and 4694 are divisors of 4694)
4694 / 2 = 2347 (the remainder is 0, so 2 and 2347 are divisors of 4694)
4694 / 3 = 1564.6666666667 (the remainder is 2, so 3 is not a divisor of 4694)
...
4694 / 67 = 70.059701492537 (the remainder is 4, so 67 is not a divisor of 4694)
4694 / 68 = 69.029411764706 (the remainder is 2, so 68 is not a divisor of 4694)