What are the divisors of 3478?

1, 2, 37, 47, 74, 94, 1739, 3478

There is a total of 8 positive divisors.
The sum of these divisors is 5472.
The arithmetic mean is 684.

4 even divisors

2, 74, 94, 3478

4 odd divisors

1, 37, 47, 1739

How to compute the divisors of 3478?

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 3478 by each of the numbers from 1 to 3478 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)

3478 / 1 = 3478 (the remainder is 0, so 1 is a divisor of 3478)
3478 / 2 = 1739 (the remainder is 0, so 2 is a divisor of 3478)
3478 / 3 = 1159.3333333333 (the remainder is 1, so 3 is not a divisor of 3478)
...
3478 / 3477 = 1.0002876042565 (the remainder is 1, so 3477 is not a divisor of 3478)
3478 / 3478 = 1 (the remainder is 0, so 3478 is a divisor of 3478)

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 3478 (i.e. 58.974570791147). 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 $\frac{N}{d} = D$ )

3478 / 1 = 3478 (the remainder is 0, so 1 and 3478 are divisors of 3478)
3478 / 2 = 1739 (the remainder is 0, so 2 and 1739 are divisors of 3478)
3478 / 3 = 1159.3333333333 (the remainder is 1, so 3 is not a divisor of 3478)
...
3478 / 57 = 61.017543859649 (the remainder is 1, so 57 is not a divisor of 3478)
3478 / 58 = 59.965517241379 (the remainder is 56, so 58 is not a divisor of 3478)