#### Programming Example

Write a program to input a number and check whether it is a Smith number or not. Smith number is such a number, the sum of whose digits equals the sum of the digits of its prime factors.

Smith number is a composite number in which the sum of its digits is equal to the sum of the digits of all its prime factors.

For Example 378 is a Smith Number as the sum of the digits of 378 are : 3+7+8 = 18. The prime factors of 378 are: 2, 3, 3, 3, 7 ( sum = 2+3+3+3+7 = 18).

Similarly 22 is a Smith Number as the sum of the digits are : 2+2=4. The prime factors of 22 are:

2 and 11 (Sum = 2+(1+1) = 4

Other Examples include 27, 58, 85, 94, 121, 166, 202, 265, etc.

`Solution`

```import java.util.*;
class SmithNumber
{
public static void main(string arr[])
{
Scanner sc=new Scanner(System.in);
int n,f=2,m,t,s1=0,s2=0,d;
System.out.println(“Enter a number:”);
n=sc.nextInt();
m=n;
while(n>1)
{
if(n%f==0)
{
t=f;
while(t!=0)
{
d=t%10;
s1+=d;
t/=10;
}
n=n/f;
}
else
f++;
}
t=m;
while(t!=0)
{
d=t%10;
s2+=d;
t/=10;
}
if(s1==s2)
System.out.println(“Smith Number”);
else
System.out.println(“Not a Smith Number”);
}
}```
`Output`