What are the divisors of 139?

1, 139

There is a total of 2 positive divisors.
The sum of these divisors is 140.
The arithmetic mean is 70.

2 odd divisors

1, 139

How to compute the divisors of 139?

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 139 by each of the numbers from 1 to 139 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)

139 / 1 = 139 (the remainder is 0, so 1 is a divisor of 139)
139 / 2 = 69.5 (the remainder is 1, so 2 is not a divisor of 139)
139 / 3 = 46.333333333333 (the remainder is 1, so 3 is not a divisor of 139)
...
139 / 138 = 1.0072463768116 (the remainder is 1, so 138 is not a divisor of 139)
139 / 139 = 1 (the remainder is 0, so 139 is a divisor of 139)

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 139 (i.e. 11.789826122552). 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 $\frac{N}{d} = D$ )

139 / 1 = 139 (the remainder is 0, so 1 and 139 are divisors of 139)
139 / 2 = 69.5 (the remainder is 1, so 2 is not a divisor of 139)
139 / 3 = 46.333333333333 (the remainder is 1, so 3 is not a divisor of 139)
...
139 / 10 = 13.9 (the remainder is 9, so 10 is not a divisor of 139)
139 / 11 = 12.636363636364 (the remainder is 7, so 11 is not a divisor of 139)