What are the divisors of 1754?

1, 2, 877, 1754

There is a total of 4 positive divisors.
The sum of these divisors is 2634.
The arithmetic mean is 658.5.

2 even divisors

2, 1754

2 odd divisors

1, 877

How to compute the divisors of 1754?

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 1754 by each of the numbers from 1 to 1754 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)

1754 / 1 = 1754 (the remainder is 0, so 1 is a divisor of 1754)
1754 / 2 = 877 (the remainder is 0, so 2 is a divisor of 1754)
1754 / 3 = 584.66666666667 (the remainder is 2, so 3 is not a divisor of 1754)
...
1754 / 1753 = 1.000570450656 (the remainder is 1, so 1753 is not a divisor of 1754)
1754 / 1754 = 1 (the remainder is 0, so 1754 is a divisor of 1754)

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 1754 (i.e. 41.880783182744). 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 $\frac{N}{d} = D$ )

1754 / 1 = 1754 (the remainder is 0, so 1 and 1754 are divisors of 1754)
1754 / 2 = 877 (the remainder is 0, so 2 and 877 are divisors of 1754)
1754 / 3 = 584.66666666667 (the remainder is 2, so 3 is not a divisor of 1754)
...
1754 / 40 = 43.85 (the remainder is 34, so 40 is not a divisor of 1754)
1754 / 41 = 42.780487804878 (the remainder is 32, so 41 is not a divisor of 1754)