What are the divisors of 1220?

1, 2, 4, 5, 10, 20, 61, 122, 244, 305, 610, 1220

There is a total of 12 positive divisors.
The sum of these divisors is 2604.
The arithmetic mean is 217.

8 even divisors

2, 4, 10, 20, 122, 244, 610, 1220

4 odd divisors

1, 5, 61, 305

How to compute the divisors of 1220?

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 1220 by each of the numbers from 1 to 1220 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)

1220 / 1 = 1220 (the remainder is 0, so 1 is a divisor of 1220)
1220 / 2 = 610 (the remainder is 0, so 2 is a divisor of 1220)
1220 / 3 = 406.66666666667 (the remainder is 2, so 3 is not a divisor of 1220)
...
1220 / 1219 = 1.0008203445447 (the remainder is 1, so 1219 is not a divisor of 1220)
1220 / 1220 = 1 (the remainder is 0, so 1220 is a divisor of 1220)

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 1220 (i.e. 34.928498393146). 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 $\frac{N}{d} = D$ )

1220 / 1 = 1220 (the remainder is 0, so 1 and 1220 are divisors of 1220)
1220 / 2 = 610 (the remainder is 0, so 2 and 610 are divisors of 1220)
1220 / 3 = 406.66666666667 (the remainder is 2, so 3 is not a divisor of 1220)
...
1220 / 33 = 36.969696969697 (the remainder is 32, so 33 is not a divisor of 1220)
1220 / 34 = 35.882352941176 (the remainder is 30, so 34 is not a divisor of 1220)