What are the divisors of 141?

1, 3, 47, 141

There is a total of 4 positive divisors.
The sum of these divisors is 192.
The arithmetic mean is 48.

4 odd divisors

1, 3, 47, 141

How to compute the divisors of 141?

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 141 by each of the numbers from 1 to 141 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)

141 / 1 = 141 (the remainder is 0, so 1 is a divisor of 141)
141 / 2 = 70.5 (the remainder is 1, so 2 is not a divisor of 141)
141 / 3 = 47 (the remainder is 0, so 3 is a divisor of 141)
...
141 / 140 = 1.0071428571429 (the remainder is 1, so 140 is not a divisor of 141)
141 / 141 = 1 (the remainder is 0, so 141 is a divisor of 141)

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 141 (i.e. 11.874342087038). 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 $\frac{N}{d} = D$ )

141 / 1 = 141 (the remainder is 0, so 1 and 141 are divisors of 141)
141 / 2 = 70.5 (the remainder is 1, so 2 is not a divisor of 141)
141 / 3 = 47 (the remainder is 0, so 3 and 47 are divisors of 141)
...
141 / 10 = 14.1 (the remainder is 1, so 10 is not a divisor of 141)
141 / 11 = 12.818181818182 (the remainder is 9, so 11 is not a divisor of 141)