What are the divisors of 2945?

1, 5, 19, 31, 95, 155, 589, 2945

There is a total of 8 positive divisors.
The sum of these divisors is 3840.
The arithmetic mean is 480.

8 odd divisors

1, 5, 19, 31, 95, 155, 589, 2945

How to compute the divisors of 2945?

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 2945 by each of the numbers from 1 to 2945 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)

2945 / 1 = 2945 (the remainder is 0, so 1 is a divisor of 2945)
2945 / 2 = 1472.5 (the remainder is 1, so 2 is not a divisor of 2945)
2945 / 3 = 981.66666666667 (the remainder is 2, so 3 is not a divisor of 2945)
...
2945 / 2944 = 1.000339673913 (the remainder is 1, so 2944 is not a divisor of 2945)
2945 / 2945 = 1 (the remainder is 0, so 2945 is a divisor of 2945)

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 2945 (i.e. 54.267854204861). 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 $\frac{N}{d} = D$ )

2945 / 1 = 2945 (the remainder is 0, so 1 and 2945 are divisors of 2945)
2945 / 2 = 1472.5 (the remainder is 1, so 2 is not a divisor of 2945)
2945 / 3 = 981.66666666667 (the remainder is 2, so 3 is not a divisor of 2945)
...
2945 / 53 = 55.566037735849 (the remainder is 30, so 53 is not a divisor of 2945)
2945 / 54 = 54.537037037037 (the remainder is 29, so 54 is not a divisor of 2945)