What are the divisors of 980?

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980

There is a total of 18 positive divisors.
The sum of these divisors is 2394.
The arithmetic mean is 133.

12 even divisors

2, 4, 10, 14, 20, 28, 70, 98, 140, 196, 490, 980

6 odd divisors

1, 5, 7, 35, 49, 245

How to compute the divisors of 980?

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 980 by each of the numbers from 1 to 980 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)

980 / 1 = 980 (the remainder is 0, so 1 is a divisor of 980)
980 / 2 = 490 (the remainder is 0, so 2 is a divisor of 980)
980 / 3 = 326.66666666667 (the remainder is 2, so 3 is not a divisor of 980)
...
980 / 979 = 1.0010214504597 (the remainder is 1, so 979 is not a divisor of 980)
980 / 980 = 1 (the remainder is 0, so 980 is a divisor of 980)

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 980 (i.e. 31.304951684997). 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 $\frac{N}{d} = D$ )

980 / 1 = 980 (the remainder is 0, so 1 and 980 are divisors of 980)
980 / 2 = 490 (the remainder is 0, so 2 and 490 are divisors of 980)
980 / 3 = 326.66666666667 (the remainder is 2, so 3 is not a divisor of 980)
...
980 / 30 = 32.666666666667 (the remainder is 20, so 30 is not a divisor of 980)
980 / 31 = 31.612903225806 (the remainder is 19, so 31 is not a divisor of 980)