What are the divisors of 1450?

1, 2, 5, 10, 25, 29, 50, 58, 145, 290, 725, 1450

There is a total of 12 positive divisors.
The sum of these divisors is 2790.
The arithmetic mean is 232.5.

6 even divisors

2, 10, 50, 58, 290, 1450

6 odd divisors

1, 5, 25, 29, 145, 725

How to compute the divisors of 1450?

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 1450 by each of the numbers from 1 to 1450 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)

1450 / 1 = 1450 (the remainder is 0, so 1 is a divisor of 1450)
1450 / 2 = 725 (the remainder is 0, so 2 is a divisor of 1450)
1450 / 3 = 483.33333333333 (the remainder is 1, so 3 is not a divisor of 1450)
...
1450 / 1449 = 1.0006901311249 (the remainder is 1, so 1449 is not a divisor of 1450)
1450 / 1450 = 1 (the remainder is 0, so 1450 is a divisor of 1450)

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 1450 (i.e. 38.07886552932). 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 $\frac{N}{d} = D$ )

1450 / 1 = 1450 (the remainder is 0, so 1 and 1450 are divisors of 1450)
1450 / 2 = 725 (the remainder is 0, so 2 and 725 are divisors of 1450)
1450 / 3 = 483.33333333333 (the remainder is 1, so 3 is not a divisor of 1450)
...
1450 / 37 = 39.189189189189 (the remainder is 7, so 37 is not a divisor of 1450)
1450 / 38 = 38.157894736842 (the remainder is 6, so 38 is not a divisor of 1450)