What are the divisors of 3494?

1, 2, 1747, 3494

There is a total of 4 positive divisors.
The sum of these divisors is 5244.
The arithmetic mean is 1311.

2 even divisors

2, 3494

2 odd divisors

1, 1747

How to compute the divisors of 3494?

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 3494 by each of the numbers from 1 to 3494 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)

3494 / 1 = 3494 (the remainder is 0, so 1 is a divisor of 3494)
3494 / 2 = 1747 (the remainder is 0, so 2 is a divisor of 3494)
3494 / 3 = 1164.6666666667 (the remainder is 2, so 3 is not a divisor of 3494)
...
3494 / 3493 = 1.0002862868594 (the remainder is 1, so 3493 is not a divisor of 3494)
3494 / 3494 = 1 (the remainder is 0, so 3494 is a divisor of 3494)

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 3494 (i.e. 59.110066824527). 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 $\frac{N}{d} = D$ )

3494 / 1 = 3494 (the remainder is 0, so 1 and 3494 are divisors of 3494)
3494 / 2 = 1747 (the remainder is 0, so 2 and 1747 are divisors of 3494)
3494 / 3 = 1164.6666666667 (the remainder is 2, so 3 is not a divisor of 3494)
...
3494 / 58 = 60.241379310345 (the remainder is 14, so 58 is not a divisor of 3494)
3494 / 59 = 59.220338983051 (the remainder is 13, so 59 is not a divisor of 3494)