You will be given some decimal digits in a int[] digits. Build an integer with the minimum possible number of factors, using each of the digits exactly once (be sure to count all factors, not only the prime factors). If more than one number has the same (minimum) number of factors, return the smallest one among them.

FewestFactors.java

public class FewestFactors {
	public static int number(int[] digits){
		LinkedList<Integer> adapter= new LinkedList<Integer>();
		for(int i=digits.length-1;i>=0;i--)
			adapter.addFirst(digits[i]);
		HashSet<LinkedList<Integer>> combinitions=combinate(adapter);
		int min=Integer.MAX_VALUE;
		int min_num=0;
		for(LinkedList<Integer> c:combinitions){
			int num=convertToInteger(c);
			int factors=2;
			for(int i=2;i<=num/2;i++){
				if(num%i==0) factors++;
			}
			if(factors<min){
				min=factors;
				min_num=num;
			}
			else if(factors==min){
				if(num<min_num) min_num=num;
			}
		}
		return min_num;
	}
	private static HashSet<LinkedList<Integer>> combinate(LinkedList<Integer> input){
		  if(input.size()==1){
			  HashSet<LinkedList<Integer>> b=new HashSet<LinkedList<Integer>>();
			  b.add(input);
			  return b;
		  }
		  HashSet<LinkedList<Integer>>ret= new HashSet<LinkedList<Integer>>();
		  int len=input.size();
		  for(int i=0;i<len;i++){
			  Integer a = input.remove(i);
			  HashSet<LinkedList<Integer>>temp=combinate(new LinkedList<Integer>(input));
			  for(LinkedList<Integer> t:temp)
				  t.addFirst(a);
			  ret.addAll(temp);
			  input.add(i, a);
		  }
		  return ret;
	}
	private static int convertToInteger(LinkedList<Integer> input){
		if(input.size()==0) return 0;
		else{
			int value=(int) Math.pow(10, input.size()-1);
			value*=input.removeFirst();
			return value+convertToInteger(input);
			
		}
	}
}

FewestFactorsTest.java

public class FewestFactorsTest {
	@Test
	public void testNumber() {
		assertEquals(21, FewestFactors.number(new int[]{1,2}));
		assertEquals(6, FewestFactors.number(new int[]{6, 0}));
		assertEquals(447, FewestFactors.number(new int[]{4, 7, 4}));
		assertEquals(1973, FewestFactors.number(new int[]{1, 3, 7, 9}));
		assertEquals(1973, FewestFactors.number(new int[]{1, 3, 7, 9}));
		assertEquals(241, FewestFactors.number(new int[]{1,2,4}));
	}
}