What are the divisors of 1377?

1, 3, 9, 17, 27, 51, 81, 153, 459, 1377

There is a total of 10 positive divisors.
The sum of these divisors is 2178.
The arithmetic mean is 217.8.

10 odd divisors

1, 3, 9, 17, 27, 51, 81, 153, 459, 1377

How to compute the divisors of 1377?

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 1377 by each of the numbers from 1 to 1377 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)

1377 / 1 = 1377 (the remainder is 0, so 1 is a divisor of 1377)
1377 / 2 = 688.5 (the remainder is 1, so 2 is not a divisor of 1377)
1377 / 3 = 459 (the remainder is 0, so 3 is a divisor of 1377)
...
1377 / 1376 = 1.000726744186 (the remainder is 1, so 1376 is not a divisor of 1377)
1377 / 1377 = 1 (the remainder is 0, so 1377 is a divisor of 1377)

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 1377 (i.e. 37.107950630559). 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 $\frac{N}{d} = D$ )

1377 / 1 = 1377 (the remainder is 0, so 1 and 1377 are divisors of 1377)
1377 / 2 = 688.5 (the remainder is 1, so 2 is not a divisor of 1377)
1377 / 3 = 459 (the remainder is 0, so 3 and 459 are divisors of 1377)
...
1377 / 36 = 38.25 (the remainder is 9, so 36 is not a divisor of 1377)
1377 / 37 = 37.216216216216 (the remainder is 8, so 37 is not a divisor of 1377)