What are the divisors of 1772?

1, 2, 4, 443, 886, 1772

There is a total of 6 positive divisors.
The sum of these divisors is 3108.
The arithmetic mean is 518.

4 even divisors

2, 4, 886, 1772

2 odd divisors

1, 443

How to compute the divisors of 1772?

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 1772 by each of the numbers from 1 to 1772 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)

1772 / 1 = 1772 (the remainder is 0, so 1 is a divisor of 1772)
1772 / 2 = 886 (the remainder is 0, so 2 is a divisor of 1772)
1772 / 3 = 590.66666666667 (the remainder is 2, so 3 is not a divisor of 1772)
...
1772 / 1771 = 1.0005646527386 (the remainder is 1, so 1771 is not a divisor of 1772)
1772 / 1772 = 1 (the remainder is 0, so 1772 is a divisor of 1772)

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 1772 (i.e. 42.095130359698). 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 $\frac{N}{d} = D$ )

1772 / 1 = 1772 (the remainder is 0, so 1 and 1772 are divisors of 1772)
1772 / 2 = 886 (the remainder is 0, so 2 and 886 are divisors of 1772)
1772 / 3 = 590.66666666667 (the remainder is 2, so 3 is not a divisor of 1772)
...
1772 / 41 = 43.219512195122 (the remainder is 9, so 41 is not a divisor of 1772)
1772 / 42 = 42.190476190476 (the remainder is 8, so 42 is not a divisor of 1772)