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Java Program to Check Peterson Number

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A Peterson number is a number that equals the sum of the factorials of its digits. It is also known as a strong number or a Krishnamurthy number.

145 is a Peterson number because:

1! + 4! + 5! = 1 + 24 + 120 = 145

Only four Peterson numbers exist in base 10: 1, 2, 145 and 40585.

1. Check a Peterson Number with User Input

The program splits the number into digits with % 10 and / 10, adds the factorial of each digit, and compares the total with the original number.

PetersonNumber.java 
import java.util.Scanner;

public class PetersonNumber {

    static int factorial(int n) {
        int result = 1;
        for (int i = 2; i <= n; i++) {
            result *= i;
        }
        return result;
    }

    static boolean isPeterson(int number) {
        int sum = 0;
        for (int temp = number; temp > 0; temp /= 10) {
            sum += factorial(temp % 10);
        }
        return sum == number;
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        System.out.print("Enter a number: ");
        int number = scanner.nextInt();
        scanner.close();

        System.out.println(number + (isPeterson(number) ? " is a Peterson number." : " is not a Peterson number."));
    }
}
Output 1
Enter a number: 145
145 is a Peterson number.
Output 2
Enter a number: 234
234 is not a Peterson number.

For 234: 2! + 3! + 4! = 2 + 6 + 24 = 32, which is not 234.

2. Faster Check Using Precomputed Factorials

A digit is always 0 to 9, so the ten factorials can be stored in an array once instead of being recalculated for every digit. This version prints all Peterson numbers up to 100,000.

PetersonRange.java 
public class PetersonRange {

    // FACT[d] holds d! for every digit d
    static final int[] FACT = {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880};

    static boolean isPeterson(int number) {
        int sum = 0;
        for (int temp = number; temp > 0; temp /= 10) {
            sum += FACT[temp % 10];
        }
        return sum == number;
    }

    public static void main(String[] args) {
        System.out.println("Peterson numbers from 1 to 100000:");
        for (int n = 1; n <= 100_000; n++) {
            if (isPeterson(n)) {
                System.out.print(n + " ");
            }
        }
        System.out.println();
    }
}
Output
Peterson numbers from 1 to 100000:
1 2 145 40585

3. Summary

  • A Peterson (strong) number equals the sum of the factorials of its digits, such as 145 = 1! + 4! + 5!.
  • Split the number into digits with % 10 and / 10.
  • Store the factorials of 0 to 9 in an array to avoid recalculating them.
  • The only Peterson numbers are 1, 2, 145 and 40585.

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