What are the divisors of 4945?

1, 5, 23, 43, 115, 215, 989, 4945

There is a total of 8 positive divisors.
The sum of these divisors is 6336.
The arithmetic mean is 792.

8 odd divisors

1, 5, 23, 43, 115, 215, 989, 4945

How to compute the divisors of 4945?

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 4945 by each of the numbers from 1 to 4945 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)

4945 / 1 = 4945 (the remainder is 0, so 1 is a divisor of 4945)
4945 / 2 = 2472.5 (the remainder is 1, so 2 is not a divisor of 4945)
4945 / 3 = 1648.3333333333 (the remainder is 1, so 3 is not a divisor of 4945)
...
4945 / 4944 = 1.0002022653722 (the remainder is 1, so 4944 is not a divisor of 4945)
4945 / 4945 = 1 (the remainder is 0, so 4945 is a divisor of 4945)

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 4945 (i.e. 70.320693966997). 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 $\frac{N}{d} = D$ )

4945 / 1 = 4945 (the remainder is 0, so 1 and 4945 are divisors of 4945)
4945 / 2 = 2472.5 (the remainder is 1, so 2 is not a divisor of 4945)
4945 / 3 = 1648.3333333333 (the remainder is 1, so 3 is not a divisor of 4945)
...
4945 / 69 = 71.666666666667 (the remainder is 46, so 69 is not a divisor of 4945)
4945 / 70 = 70.642857142857 (the remainder is 45, so 70 is not a divisor of 4945)