What are the divisors of 3154?

1, 2, 19, 38, 83, 166, 1577, 3154

There is a total of 8 positive divisors.
The sum of these divisors is 5040.
The arithmetic mean is 630.

4 even divisors

2, 38, 166, 3154

4 odd divisors

1, 19, 83, 1577

How to compute the divisors of 3154?

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 3154 by each of the numbers from 1 to 3154 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)

3154 / 1 = 3154 (the remainder is 0, so 1 is a divisor of 3154)
3154 / 2 = 1577 (the remainder is 0, so 2 is a divisor of 3154)
3154 / 3 = 1051.3333333333 (the remainder is 1, so 3 is not a divisor of 3154)
...
3154 / 3153 = 1.000317158262 (the remainder is 1, so 3153 is not a divisor of 3154)
3154 / 3154 = 1 (the remainder is 0, so 3154 is a divisor of 3154)

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 3154 (i.e. 56.160484328396). 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 $\frac{N}{d} = D$ )

3154 / 1 = 3154 (the remainder is 0, so 1 and 3154 are divisors of 3154)
3154 / 2 = 1577 (the remainder is 0, so 2 and 1577 are divisors of 3154)
3154 / 3 = 1051.3333333333 (the remainder is 1, so 3 is not a divisor of 3154)
...
3154 / 55 = 57.345454545455 (the remainder is 19, so 55 is not a divisor of 3154)
3154 / 56 = 56.321428571429 (the remainder is 18, so 56 is not a divisor of 3154)