What are the divisors of 1877?

1, 1877

There is a total of 2 positive divisors.
The sum of these divisors is 1878.
The arithmetic mean is 939.

2 odd divisors

1, 1877

How to compute the divisors of 1877?

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 1877 by each of the numbers from 1 to 1877 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)

1877 / 1 = 1877 (the remainder is 0, so 1 is a divisor of 1877)
1877 / 2 = 938.5 (the remainder is 1, so 2 is not a divisor of 1877)
1877 / 3 = 625.66666666667 (the remainder is 2, so 3 is not a divisor of 1877)
...
1877 / 1876 = 1.0005330490405 (the remainder is 1, so 1876 is not a divisor of 1877)
1877 / 1877 = 1 (the remainder is 0, so 1877 is a divisor of 1877)

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 1877 (i.e. 43.324358044869). 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 $\frac{N}{d} = D$ )

1877 / 1 = 1877 (the remainder is 0, so 1 and 1877 are divisors of 1877)
1877 / 2 = 938.5 (the remainder is 1, so 2 is not a divisor of 1877)
1877 / 3 = 625.66666666667 (the remainder is 2, so 3 is not a divisor of 1877)
...
1877 / 42 = 44.690476190476 (the remainder is 29, so 42 is not a divisor of 1877)
1877 / 43 = 43.651162790698 (the remainder is 28, so 43 is not a divisor of 1877)