What are the divisors of 2914?

1, 2, 31, 47, 62, 94, 1457, 2914

There is a total of 8 positive divisors.
The sum of these divisors is 4608.
The arithmetic mean is 576.

4 even divisors

2, 62, 94, 2914

4 odd divisors

1, 31, 47, 1457

How to compute the divisors of 2914?

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 2914 by each of the numbers from 1 to 2914 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)

2914 / 1 = 2914 (the remainder is 0, so 1 is a divisor of 2914)
2914 / 2 = 1457 (the remainder is 0, so 2 is a divisor of 2914)
2914 / 3 = 971.33333333333 (the remainder is 1, so 3 is not a divisor of 2914)
...
2914 / 2913 = 1.0003432887058 (the remainder is 1, so 2913 is not a divisor of 2914)
2914 / 2914 = 1 (the remainder is 0, so 2914 is a divisor of 2914)

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 2914 (i.e. 53.981478305063). 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 $\frac{N}{d} = D$ )

2914 / 1 = 2914 (the remainder is 0, so 1 and 2914 are divisors of 2914)
2914 / 2 = 1457 (the remainder is 0, so 2 and 1457 are divisors of 2914)
2914 / 3 = 971.33333333333 (the remainder is 1, so 3 is not a divisor of 2914)
...
2914 / 52 = 56.038461538462 (the remainder is 2, so 52 is not a divisor of 2914)
2914 / 53 = 54.981132075472 (the remainder is 52, so 53 is not a divisor of 2914)