In java please

Objective

Note: This homework does not use polymorphism. We are going to do a math problem instead

Find the set of smallest factors that compose a number

• Example: n = 90
  • Factors = {1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 }
  • Least Factors = {2,3,3,5}
• That is, 2 * 3 * 3 * 5 = 90
• Notice these are the smallest of the factors?

Part 1

Write a method that returns a List of all factors for a variable n

What are the factors of n?

• They are the numbers from 1 to n that divide evenly into n
  • Note: No number greater than n can divide evenly into it
• You can test if something divides evenly with Modulus (%)
  • Returns the remainder of the division

Part 2

Write a Method that takes a List of factors and the number n and returns the List of smallest factors

Follow this algorithm (written in pseudocode)

• while(n != 1)
  • i = 1
  • nextDivFound = false
  • while(nextDivFound == false)
    • if factors[i] divides evenly into n
      • nextDivFound = true
      • returnList.add(factors[i])
      • n = n / factors[i]
    • else i++

Note that the factor[0] is skipped. This will contain the number 1 and will lead to an infinite loop.

Main Function

Read in the value n from the console using any method you prefer.

• Example is Scanner from java.util.*
• Scanner scan = new Scanner(System.in);
• int n = scan.nextInt();

Call your first method to find the factors then output the List it returns. Next call the second method to find the smallest factors and output the List it returns.

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