## Definition of Java Smith Number

In Java we have a different kind of functionality; the smith number is the one kind of functionality that is provided to the user. Basically, the smith number is nothing but the composite number (whose base is 10 in the number system) whose addition of all digits is equal to the addition of all digits of its all prime factor (excluding 1), this is known as the smith number. Another name for smith number is the joke number. By definition, we can say that all prime numbers are excluded naturally if they satisfy the condition. Normally smith number is a very basic subfield of the number system used in mathematics as per user requirement and some of its requirement of the problem statement.

### Logic behind smith number

Now let’s see what logic behind the smith number is as follows.

Logic of the smith number is very simple, let’s consider the following number then we will easily understand the logic as follows.

Example: Suppose we need to check if the given number is a smith number or not.

The given number is: 95

First, we need to find out the primes factor of 95 is 19 and 5 (5, 19)

Now find the sum of digit that is 9 + 5 = 14

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Sum of prime factor is 5 + 1 + 9 = 15

Now compare both results, see here 14 is not equal to 15. So the given number is not a prime number.

Let’s consider another number as follows.

Given number: 58

First find the primes factor of 58 = 2 and 29

Sum of prime factor is = 2 + 2 +9 = 13

Sum of given number digit is = 5 + 8 = 13

Now compare both results, here both results are same or we can say that is equal. So we can say that the given number is the smith number.

So this is the very simple logic behind the smith number, we just need to compare the prime factorial sum and digit sum. If both sums are equal then the given number is the smith number otherwise the number is not a smith number.

### How to Check Smith number in Java?

Now let’s see how we can check if a given number is smith or not in java as follows.

In the above point, we already discussed different examples of smith numbers. Now let’s see the different steps to find the smith number as follows.

1. First we need to initialize or read numbers from the user.

2. After that we need to find the sum of the digits of the given number.

3. Next we need to find the primes factor of a given number.

4. Now calculate the sum of digits of prime factors.

5. Now compare the sum of digits of a given number and sum of digits of prime factors.

a. If both sums are equal then we can say that the given number is the smith number.

b. Else, we can consider a given number is not a smith number because sums are different.

So the above-mentioned steps are useful to implement smith number programs in Java.

### Examples

Now let’s see the different examples of smith numbers in java for better understanding as follows.

#### Example #1

**Code:**

```
import java.util.*;
public class Smith_Num
{
static int F_Sum_P_Fact(int no)
{
int j=2, add=0;
while(no>1)
{
if(no%j==0)
{
add=add+F_S_Digit(j);
no=no/j;
}
else
{
do
{
j++;
}
while(!isPrime(j));
}
}
return add;
}
static int F_S_Digit(int no)
{
int sum=0;
while(no>0)
{
sum=sum+no%10;
no=no/10;
}
return sum;
}
static boolean isPrime(int j)
{
boolean b=true;
int d=2;
while(d<Math.sqrt(j))
{
if(j%d==0)
{
b=false;
}
d++;
}
return b;
}
public static void main(String args[])
{
Scanner s_c = new Scanner(System.in);
System.out.print("Enter a number: ");
int no=s_c.nextInt();
int x = F_S_Digit(no);
int y = F_Sum_P_Fact(no);
System.out.println("addition of digit = "+x);
System.out.println("addition of prime factors digits is = "+y);
if(x==y)
System.out.print("The user enterd number is smith number.");
else
System. out.print("The user entered number is not smith number.");
}
}
```

**Explanation**

In the above program, we try to implement the smith number program in java. Here we first created the function to sum of digits of prime factors; similarly, we also created the function to find the sum of digits for the given number as shown in the above program. After that, we created the function to check if the given number is a prime number or not by using Boolean functions. Then we write the main function, inside the main function we accept the number from the user and call all function which we already created and compare both sums. If the sum is equal then print the given number as smith number and if the sum is not equal then print the given number is not smith number. The final output of the above program we illustrate by using the following screenshot as follows.

#### Example #2

Let’s see another example as follows.

**Code:**

```
import java.util.*;
public class Smith_Num_2
{
static List<Integer> F_P_Fact(int no)
{
List<Integer> output = new ArrayList<>();
for (int j = 2; no % j == 0; no = no/j)
output.add(j);
for (int j = 3; j* j <= no; j=j+2)
{
while (no % j == 0)
{
output.add(j);
no = no/j;
}
}
if (no != 1)
output.add(no);
return output;
}
static int S_Digit(int no)
{
int s= 0;
while (no > 0)
{
s =s+(no % 10);
no = no/10;
}
return s;
}
public static void main(String args[])
{
for (int no = 1; no < 5000; no++)
{
List<Integer> Fact = F_P_Fact(no);
if (Fact.size() > 1)
{
int s = S_Digit(no);
for (int fa : Fact)
s =s-S_Digit(fa);
if (s == 0)
System.out.println(no);
}
}
}
}
```

**Explanation**

In the above example, we try to find out the all smith number up to 5000 as shown. The final output of the above program we illustrate by using the following screenshot as follows.

### Conclusion

We hope from this article you learn Smith Number in java. From the above article, we have learned the basic logic of Smith Number and we also see different examples of Smith Number. From this article, we learned how and when we use the Smith Number in java.

### Recommended Articles

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