What are the divisors of 484?

1, 2, 4, 11, 22, 44, 121, 242, 484

There is a total of 9 positive divisors.
The sum of these divisors is 931.
The arithmetic mean is 103.44444444444.

6 even divisors

2, 4, 22, 44, 242, 484

3 odd divisors

1, 11, 121

How to compute the divisors of 484?

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 484 by each of the numbers from 1 to 484 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)

484 / 1 = 484 (the remainder is 0, so 1 is a divisor of 484)
484 / 2 = 242 (the remainder is 0, so 2 is a divisor of 484)
484 / 3 = 161.33333333333 (the remainder is 1, so 3 is not a divisor of 484)
...
484 / 483 = 1.0020703933747 (the remainder is 1, so 483 is not a divisor of 484)
484 / 484 = 1 (the remainder is 0, so 484 is a divisor of 484)

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 484 (i.e. 22). 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 $\frac{N}{d} = D$ )

484 / 1 = 484 (the remainder is 0, so 1 and 484 are divisors of 484)
484 / 2 = 242 (the remainder is 0, so 2 and 242 are divisors of 484)
484 / 3 = 161.33333333333 (the remainder is 1, so 3 is not a divisor of 484)
...
484 / 21 = 23.047619047619 (the remainder is 1, so 21 is not a divisor of 484)
484 / 22 = 22 (the remainder is 0, so 22 and 22 are divisors of 484)