R Examples

R Program - Find all factors of a Number

Objective: Write a R program to find all distinct factors (divisors) of a given natural number. The divisors of few numbers are given below:

 Number: 10
 Divisors: 1 2 5 10

 Number: 15
 Divisors: 1 3 5 15

 Number: 100
 Divisors: 1 2 4 5 10 20 25 50 100

Method 1: Using iteration

One of the basic approach is to iterate from 1 to n and in each iteration check whether the number divides n. If it divides then print it.

#function to print all divisors of a number
printDivisors <- function(n) {
  cat("Divisors of", n ,"are: ")

  #creating vector to store all divisors
  divisors <- c()
  for (i in c(1:n)) {
    if(n%%i == 0) {
      #storing all divisors
      divisors <- c(divisors, i)
    }
  }
  cat(divisors, "\n")  
}

printDivisors(10)
printDivisors(50)
printDivisors(100)

The above code will give the following output:

Divisors of 10 are: 1 2 5 10 
Divisors of 50 are: 1 2 5 10 25 50 
Divisors of 100 are: 1 2 4 5 10 20 25 50 100

Method 2: Optimized Code

Instead of checking the divisibility of the given number from 1 to n, it is checked till square root of n. For a factor larger than square root of n, there must the a smaller factor which is already checked in the range of 1 to square root of n.

#function to print all divisors of a number
printDivisors <- function(n) {
  cat("Divisors of", n ,"are: ")

  #creating vector to store all divisors
  divisors <- c()

  #loop from 1 to sqrt(n)
  for (i in c(1:sqrt(n))) {
    if(n%%i == 0) {
      #storing all divisors
      if(n%/%i == i) {
        divisors <- c(divisors, i)
      } else {
        divisors <- c(divisors, i, n%/%i)
      }      
    }
  }
  cat(divisors, "\n")  
}

printDivisors(10)
printDivisors(50)
printDivisors(100)

The above code will give the following output:

Divisors of 10 are: 1 10 2 5 
Divisors of 50 are: 1 50 2 25 5 10 
Divisors of 100 are: 1 100 2 50 4 25 5 20 10

Method 3: Optimized Code with sorted result

In the previous method, results are produced in a irregular fashion (printed in pairs - small number and large number). The result can be sorted by using R sort() function. Consider the example below:

#function to print all divisors of a number
printDivisors <- function(n) {
  cat("Divisors of", n ,"are: ")

  #creating vector to store all divisors
  divisors <- c()

  #loop from 1 to sqrt(n)
  for (i in c(1:sqrt(n))) {
    if(n%%i == 0) {
      #storing all divisors
      if(n%/%i == i) {
        divisors <- c(divisors, i)
      } else {
        divisors <- c(divisors, i, n%/%i)
      }      
    }
  }
  divisors <- sort(divisors)
  cat(divisors, "\n")  
}

printDivisors(10)
printDivisors(50)
printDivisors(100)

The above code will give the following output:

Divisors of 10 are: 1 2 5 10 
Divisors of 50 are: 1 2 5 10 25 50 
Divisors of 100 are: 1 2 4 5 10 20 25 50 100