What are the divisors of 2980?

1, 2, 4, 5, 10, 20, 149, 298, 596, 745, 1490, 2980

There is a total of 12 positive divisors.
The sum of these divisors is 6300.
The arithmetic mean is 525.

8 even divisors

2, 4, 10, 20, 298, 596, 1490, 2980

4 odd divisors

1, 5, 149, 745

How to compute the divisors of 2980?

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 2980 by each of the numbers from 1 to 2980 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)

2980 / 1 = 2980 (the remainder is 0, so 1 is a divisor of 2980)
2980 / 2 = 1490 (the remainder is 0, so 2 is a divisor of 2980)
2980 / 3 = 993.33333333333 (the remainder is 1, so 3 is not a divisor of 2980)
...
2980 / 2979 = 1.0003356831151 (the remainder is 1, so 2979 is not a divisor of 2980)
2980 / 2980 = 1 (the remainder is 0, so 2980 is a divisor of 2980)

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 2980 (i.e. 54.589376255825). 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 $\frac{N}{d} = D$ )

2980 / 1 = 2980 (the remainder is 0, so 1 and 2980 are divisors of 2980)
2980 / 2 = 1490 (the remainder is 0, so 2 and 1490 are divisors of 2980)
2980 / 3 = 993.33333333333 (the remainder is 1, so 3 is not a divisor of 2980)
...
2980 / 53 = 56.22641509434 (the remainder is 12, so 53 is not a divisor of 2980)
2980 / 54 = 55.185185185185 (the remainder is 10, so 54 is not a divisor of 2980)