What are the divisors of 3274?

1, 2, 1637, 3274

There is a total of 4 positive divisors.
The sum of these divisors is 4914.
The arithmetic mean is 1228.5.

2 even divisors

2, 3274

2 odd divisors

1, 1637

How to compute the divisors of 3274?

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 3274 by each of the numbers from 1 to 3274 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)

3274 / 1 = 3274 (the remainder is 0, so 1 is a divisor of 3274)
3274 / 2 = 1637 (the remainder is 0, so 2 is a divisor of 3274)
3274 / 3 = 1091.3333333333 (the remainder is 1, so 3 is not a divisor of 3274)
...
3274 / 3273 = 1.0003055300947 (the remainder is 1, so 3273 is not a divisor of 3274)
3274 / 3274 = 1 (the remainder is 0, so 3274 is a divisor of 3274)

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 3274 (i.e. 57.21887800368). 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 $\frac{N}{d} = D$ )

3274 / 1 = 3274 (the remainder is 0, so 1 and 3274 are divisors of 3274)
3274 / 2 = 1637 (the remainder is 0, so 2 and 1637 are divisors of 3274)
3274 / 3 = 1091.3333333333 (the remainder is 1, so 3 is not a divisor of 3274)
...
3274 / 56 = 58.464285714286 (the remainder is 26, so 56 is not a divisor of 3274)
3274 / 57 = 57.438596491228 (the remainder is 25, so 57 is not a divisor of 3274)