What are the divisors of 177?

1, 3, 59, 177

There is a total of 4 positive divisors.
The sum of these divisors is 240.
The arithmetic mean is 60.

4 odd divisors

1, 3, 59, 177

How to compute the divisors of 177?

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 177 by each of the numbers from 1 to 177 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)

177 / 1 = 177 (the remainder is 0, so 1 is a divisor of 177)
177 / 2 = 88.5 (the remainder is 1, so 2 is not a divisor of 177)
177 / 3 = 59 (the remainder is 0, so 3 is a divisor of 177)
...
177 / 176 = 1.0056818181818 (the remainder is 1, so 176 is not a divisor of 177)
177 / 177 = 1 (the remainder is 0, so 177 is a divisor of 177)

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 177 (i.e. 13.30413469565). 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 $\frac{N}{d} = D$ )

177 / 1 = 177 (the remainder is 0, so 1 and 177 are divisors of 177)
177 / 2 = 88.5 (the remainder is 1, so 2 is not a divisor of 177)
177 / 3 = 59 (the remainder is 0, so 3 and 59 are divisors of 177)
...
177 / 12 = 14.75 (the remainder is 9, so 12 is not a divisor of 177)
177 / 13 = 13.615384615385 (the remainder is 8, so 13 is not a divisor of 177)