Smith Number in Java

In this section, we will learn what is a smith number and also create Java programs to check if the given number is smith or not. The smith number program frequently asked in Java coding tests and academics.

Smith Number

A Smith number is a composite number whose sum of digits equals to the sum of digits of its prime factors, excluding 1. It is also known as a joke number. It is a sequence of OEIS A006753.

Sum of digits of n = Sum of digits of prime factors of n (counted with multiplicity)

Let's understand it through an example.

Smith Number Example

Example 1: Suppose, we want to check the number 85 is smith or not.

Sum of digits = 8 + 5 = 13

Prime factors of 85 is: 5,17

Sum of digits of its prime factors = 5 + 1+ 7 = 13

Compare the sum of digits with the sum of digits of its prime factors i.e. 13=13. Both are equal. Hence, the given number (85) is a smith number.

Example 2: Let's check another number 999 is smith or not.

Sum of digits = 9+ 9+9 = 27

Prime factors of 999 is: 3×3×3,37

Sum of digits of its prime factors = 3+3+3+3+7 =19

Compare the sum of digits with the sum of digits of its prime factors i.e. 27≠19. Hence, the given number (999) is not a smith number.

Similarly, we can check other numbers also. Some other smith numbers are 4, 27, 85, 94, 121, 166, 202, 265, 274, 319, 346, 666, etc.

Steps to Find Smith Number

Read or initialize a number from the user.
Find the sum of its digits.
Find the prime factors of the given number.
Determine the sum of digits of its prime factors.
Compare the sum of digits with the sum of digits of its prime factors.
- If they are equal, the given number is a smith
- Else, not a smith number.

Let's implement the above steps in a Java program.

Smith Number Java Program

SmithNumberExample1.java

import java.util.*;
public class SmithNumberExample1
{
//function finds the sum of digits of its prime factors
static int findSumPrimeFactors(int n)
{
int i=2, sum=0;
while(n>1)
{
if(n%i==0)
{
sum=sum+findSumOfDigit(i);
n=n/i;
}
else
{
do
{
i++;
}
while(!isPrime(i));
}
}
//returns the sum of digits of prime factors
return sum;
}
//function finds the sum of digits of the given numbers
static int findSumOfDigit(int n)
{
//stores the sum
int s=0;
while(n>0)
{
//finds the last digit of the number and add it to the variable s    
s=s+n%10;
//removes the last digit from the given number
n=n/10;
}
//returns the sum of digits of the number
return s;
}
//function checks if the factor is prime or not
static boolean isPrime(int k)
{
boolean b=true;
int d=2;
while(d<Math.sqrt(k))
{
if(k%d==0)
{
b=false;
}
d++;
}
return b;
}
//driver code
public static void main(String args[])
{
Scanner sc = new Scanner(System.in);
System.out.print("Enter a number: ");
//reads an integer from the user
int n=sc.nextInt();
//calling the user-defined function that finds the sum of digits of the given number
int a = findSumOfDigit(n);
//calling the user-defined function that finds the sum of prime factors
int b = findSumPrimeFactors(n);
System.out.println("Sum of Digits of the given number is = "+a);
System.out.println("Sum of digits of its prime factors is = "+b);
//compare both the sums
if(a==b)
//prints if above condition returns true
System.out.print("The given number is a smith number.");
//prints if above condition returns false
else
System.out.print("The given number is not a smith number.");
}
}

Output 1:

Output 2:

Let's create a Java program that finds all the smith numbers up to 10,000.

SmithNumberExample2.java

import java.util.*;
public class SmithNumberExample2 
{
//function finds all the prime factors for the given number
static List<Integer> findPrimeFactors(int n) 
{
//creating an array list that stores the prime factors    
List<Integer> result = new ArrayList<>();
for (int i = 2; n % i == 0; n = n/i)
result.add(i);
for (int i = 3; i * i <= n; i =i+2) 
{
while (n % i == 0) 
{
result.add(i);
n = n/i;
}
}
if (n != 1)
//the add() method adds the prime factors to the list
result.add(n);
return result;
}
//function finds the sum of digits of the given number
static int sumOfDigits(int n) 
{
int sum = 0;
while (n > 0) 
{
//finds the last digit and add it to the sum    
sum =sum+(n % 10);
//removes the last digit from the number
n = n/10;
}
//returns the sum of digits
return sum;
}
//driver code    
public static void main(String args[]) 
{
//finds all smit numbers up to 10000    
for (int n = 1; n < 10000; n++) 
{
//calling the user-defined function that finds prime factors
List<Integer> factors = findPrimeFactors(n);
//the size() method returns the number of elements in the list
//executes until the condition becomes false
if (factors.size() > 1) 
{
int sum = sumOfDigits(n);
for (int f : factors)
sum =sum-sumOfDigits(f);
if (sum == 0)
System.out.println(n);
}
}
}
}

Output:

4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454, 483, 517, 526, 535, 562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 861, 895, 913, 915, 922, 958, 985, 1086, 1111, 1165, 1219, 1255, 1282, 1284, 1376, 1449, 1507, 1581, 1626, 1633, 1642, 1678, 1736, 1755, 1776, 1795, 1822