What are the divisors of 3479?

1, 7, 49, 71, 497, 3479

There is a total of 6 positive divisors.
The sum of these divisors is 4104.
The arithmetic mean is 684.

6 odd divisors

1, 7, 49, 71, 497, 3479

How to compute the divisors of 3479?

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 3479 by each of the numbers from 1 to 3479 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)

3479 / 1 = 3479 (the remainder is 0, so 1 is a divisor of 3479)
3479 / 2 = 1739.5 (the remainder is 1, so 2 is not a divisor of 3479)
3479 / 3 = 1159.6666666667 (the remainder is 2, so 3 is not a divisor of 3479)
...
3479 / 3478 = 1.0002875215641 (the remainder is 1, so 3478 is not a divisor of 3479)
3479 / 3479 = 1 (the remainder is 0, so 3479 is a divisor of 3479)

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 3479 (i.e. 58.983048412235). 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 $\frac{N}{d} = D$ )

3479 / 1 = 3479 (the remainder is 0, so 1 and 3479 are divisors of 3479)
3479 / 2 = 1739.5 (the remainder is 1, so 2 is not a divisor of 3479)
3479 / 3 = 1159.6666666667 (the remainder is 2, so 3 is not a divisor of 3479)
...
3479 / 57 = 61.035087719298 (the remainder is 2, so 57 is not a divisor of 3479)
3479 / 58 = 59.98275862069 (the remainder is 57, so 58 is not a divisor of 3479)