What are the divisors of 490?

1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490

There is a total of 12 positive divisors.
The sum of these divisors is 1026.
The arithmetic mean is 85.5.

6 even divisors

2, 10, 14, 70, 98, 490

6 odd divisors

1, 5, 7, 35, 49, 245

How to compute the divisors of 490?

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 490 by each of the numbers from 1 to 490 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)

490 / 1 = 490 (the remainder is 0, so 1 is a divisor of 490)
490 / 2 = 245 (the remainder is 0, so 2 is a divisor of 490)
490 / 3 = 163.33333333333 (the remainder is 1, so 3 is not a divisor of 490)
...
490 / 489 = 1.0020449897751 (the remainder is 1, so 489 is not a divisor of 490)
490 / 490 = 1 (the remainder is 0, so 490 is a divisor of 490)

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 490 (i.e. 22.135943621179). 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 $\frac{N}{d} = D$ )

490 / 1 = 490 (the remainder is 0, so 1 and 490 are divisors of 490)
490 / 2 = 245 (the remainder is 0, so 2 and 245 are divisors of 490)
490 / 3 = 163.33333333333 (the remainder is 1, so 3 is not a divisor of 490)
...
490 / 21 = 23.333333333333 (the remainder is 7, so 21 is not a divisor of 490)
490 / 22 = 22.272727272727 (the remainder is 6, so 22 is not a divisor of 490)