What are the divisors of 2954?

1, 2, 7, 14, 211, 422, 1477, 2954

There is a total of 8 positive divisors.
The sum of these divisors is 5088.
The arithmetic mean is 636.

4 even divisors

2, 14, 422, 2954

4 odd divisors

1, 7, 211, 1477

How to compute the divisors of 2954?

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 2954 by each of the numbers from 1 to 2954 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)

2954 / 1 = 2954 (the remainder is 0, so 1 is a divisor of 2954)
2954 / 2 = 1477 (the remainder is 0, so 2 is a divisor of 2954)
2954 / 3 = 984.66666666667 (the remainder is 2, so 3 is not a divisor of 2954)
...
2954 / 2953 = 1.0003386386725 (the remainder is 1, so 2953 is not a divisor of 2954)
2954 / 2954 = 1 (the remainder is 0, so 2954 is a divisor of 2954)

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 2954 (i.e. 54.350712966805). 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 $\frac{N}{d} = D$ )

2954 / 1 = 2954 (the remainder is 0, so 1 and 2954 are divisors of 2954)
2954 / 2 = 1477 (the remainder is 0, so 2 and 1477 are divisors of 2954)
2954 / 3 = 984.66666666667 (the remainder is 2, so 3 is not a divisor of 2954)
...
2954 / 53 = 55.735849056604 (the remainder is 39, so 53 is not a divisor of 2954)
2954 / 54 = 54.703703703704 (the remainder is 38, so 54 is not a divisor of 2954)