What are the divisors of 1490?

1, 2, 5, 10, 149, 298, 745, 1490

There is a total of 8 positive divisors.
The sum of these divisors is 2700.
The arithmetic mean is 337.5.

4 even divisors

2, 10, 298, 1490

4 odd divisors

1, 5, 149, 745

How to compute the divisors of 1490?

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 1490 by each of the numbers from 1 to 1490 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)

1490 / 1 = 1490 (the remainder is 0, so 1 is a divisor of 1490)
1490 / 2 = 745 (the remainder is 0, so 2 is a divisor of 1490)
1490 / 3 = 496.66666666667 (the remainder is 2, so 3 is not a divisor of 1490)
...
1490 / 1489 = 1.0006715916723 (the remainder is 1, so 1489 is not a divisor of 1490)
1490 / 1490 = 1 (the remainder is 0, so 1490 is a divisor of 1490)

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 1490 (i.e. 38.600518131238). 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 $\frac{N}{d} = D$ )

1490 / 1 = 1490 (the remainder is 0, so 1 and 1490 are divisors of 1490)
1490 / 2 = 745 (the remainder is 0, so 2 and 745 are divisors of 1490)
1490 / 3 = 496.66666666667 (the remainder is 2, so 3 is not a divisor of 1490)
...
1490 / 37 = 40.27027027027 (the remainder is 10, so 37 is not a divisor of 1490)
1490 / 38 = 39.210526315789 (the remainder is 8, so 38 is not a divisor of 1490)