What are the divisors of 1510?

1, 2, 5, 10, 151, 302, 755, 1510

There is a total of 8 positive divisors.
The sum of these divisors is 2736.
The arithmetic mean is 342.

4 even divisors

2, 10, 302, 1510

4 odd divisors

1, 5, 151, 755

How to compute the divisors of 1510?

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 1510 by each of the numbers from 1 to 1510 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)

1510 / 1 = 1510 (the remainder is 0, so 1 is a divisor of 1510)
1510 / 2 = 755 (the remainder is 0, so 2 is a divisor of 1510)
1510 / 3 = 503.33333333333 (the remainder is 1, so 3 is not a divisor of 1510)
...
1510 / 1509 = 1.0006626905235 (the remainder is 1, so 1509 is not a divisor of 1510)
1510 / 1510 = 1 (the remainder is 0, so 1510 is a divisor of 1510)

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 1510 (i.e. 38.858718455451). 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 $\frac{N}{d} = D$ )

1510 / 1 = 1510 (the remainder is 0, so 1 and 1510 are divisors of 1510)
1510 / 2 = 755 (the remainder is 0, so 2 and 755 are divisors of 1510)
1510 / 3 = 503.33333333333 (the remainder is 1, so 3 is not a divisor of 1510)
...
1510 / 37 = 40.810810810811 (the remainder is 30, so 37 is not a divisor of 1510)
1510 / 38 = 39.736842105263 (the remainder is 28, so 38 is not a divisor of 1510)