Check a number is smith number or not.[ISC 2008 Practical]
Defnation: A Smith number is a composite number, the sum of whose digits is the sum of the digits of its prime factors obtained as a result of prime factorization (excluding 1). The first few such numbers are 4, 22, 27, 58, 85, 94, 121 ……………….
121 - 1 + 2 + 1 = 4
prime factors of 121 is 11 11 (excluding 1)
1 + 1 + 1 + 1 = 4
Steps to slove the problems
step 1 : Find the sum of the digits of the given numbers.
step 2 : Find the prime factors.
step 3 : Find the sum of the digits of the prime factors.
step 4 : Compare two result.
import java.util.*;
public class SmithNumbers
{
int sumDigit(int n)
{
int s=0;
while(n>0)
{
s=s+n%10;
n=n/10;
}
return s;
}
int sumPrimeFact(int n)
{
int i=2, sum=0;
while(n>1)
{
if(n%i==0)
{
sum=sum+sumDigit(i);
n=n/i;
}
else
{
do{
i++;
}while(!IsPrime(i));
}
}
return sum;
}
boolean IsPrime(int k)
{
boolean b=true;
int d=2;
while(d<Math.sqrt(k))
{
if(k%d==0)
{
b=false;
}
d++;
}
return b;
}
public static void main(String args[])
{
Scanner sc=new Scanner(System.in);
SmithNumbers ob=new SmithNumbers();
System.out.print("Enter a Number : ");
int n=sc.nextInt();
int a=ob.sumDigit(n);
int b=ob.sumPrimeFact(n);
System.out.println("Sum of Digit = "+a);
System.out.println("Sum of Prime Factor = "+b);
if(a==b)
System.out.print("It is a Smith Number");
else
System.out.print("It is Not a Smith Number");
}
}
Output:
Enter a Number : 85
Sum of Digit = 13
Sum of Prime Factor = 13
It is a Smith Number
Enter a Number : 121
Sum of Digit = 4
Sum of Prime Factor = 4
It is a Smith Number
Enter a Number : 666
Sum of Digit = 18
Sum of Prime Factor = 18
It is a Smith Number
Enter a Number : 999
Sum of Digit = 27
Sum of Prime Factor = 19
It is Not a Smith Number
