Equidigital Number in Java

In this section, we will learn what is equidigital number and also create Java programs to find the equidigital numbers. It is frequently asked in Java coding interviews and academics.

Equidigital Number

A natural number that has the same number of digits as the number of digits present in its prime factorization (including exponents) is the equidigital number in Java.

Steps to Find Equidigital Numbers

Step 1: Pick a natural number. Let's say the number is n.

Step 2: Compute the prime factorization of the number n. Store the digits involved in the prime factors of the prime factorization and its exponents in an array.

Step 3: Find the size of the array.

Step 4: Calculate the number of digits present in the number n.

Step 5: If the total number of digits present in the number n is equal to the size of the array found in step 3, then the number n is an equidigital number; otherwise, not.

Examples of Equidigital Numbers

Equidigital Number	Its Prime Factorization	Number of digits present in the number	Number of digits in the prime factorization (including exponents)
2	2	1	1
3	3	1	1
5	5	1	1
7	7	1	1
10	2 * 5	2	2
11	11	2	2 (11 has two digits)
13	13	2	2 (13 has two digits)

We see that every number mentioned in the table has the same number of digits as the number of digits present in the prime factorization (including exponents). Hence, the numbers mentioned in the above table are the equidigital numbers.

Note: 1 is not an equidigital number. Because 1 is only divisible by itself, and 1 is not a prime number.

Equidigital Numbers Java Program

The following program checks for the equidigital numbers using the steps defined above.

FileName: EquidigitalNumber.java

// A program that checks for the equidigital number from 1 to 30
import java.util.*;
public class EquidigitalNumber 
{
// the method finds the digits of the factors and their exponents found in the prime 
// factorization
public static void addDig(ArrayList<Integer> al, int no)
{
while(no != 0)
{
no = no / 10;
al.add(1);
}
}
// A method to find the all-prime factors
// of the given number no, and stores those factors in the list al
public static void findPrimeFactors(int no, ArrayList<Integer> al)
{
// Extract all the 2s present in the number and store in the list al
Boolean flag = false;
int count = 0;
while (no % 2 == 0) 
{
flag = true;
no = no / 2;
count = count + 1;
}
if(flag)
{
al.add(2);
if(count > 1)
{
// handling digits of exponents
if(count > 9)
{
addDig(al, count);    
}
else
{
al.add(count);
}
}
}
// after all the 2s are removed from the number no, the number no 
// must be odd. So we can take a jump of 2
// Notice the statement j = j + 2
// It is because 3 is odd and 3 + 2 = 5 which is also odd.
// 5 + 2 = 7, which is also odd. Thus, we see that when we 
// add 2 to an odd number we always get an odd number.
for (int j = 3; j <= Math.sqrt(no); j = j + 2) 
{
count = 0;
flag = false;
// While j divides the number no, store j and continue dividing the number no
while (no % j == 0) 
{
flag = true;
no = no / j;
count = count + 1;
}
if(flag)
{
// we have to ensure that 
// we are not considering the prime factors. We have to 
// ensure that total number of digits present 
// in the factors are considered.
if(j > 10)
{
addDig(al, j);
}
else
{
al.add(j);
}
if(count > 1)
{
// handling digits of exponents
if(count > 9)
{
addDig(al, count);    
}
else
{
al.add(count);
}
}
}
}
// if no is a prime number whose value is 
// greater than 2 then no should be included in the list.
if(no > 2)
{
if(no > 10)
{
addDig(al, no);
}
else
{
al.add(no);
}
}
}
// a method to find the total number digits 
// present in the number no.
public static int findDigits(int no)
{
int dig = 0;
while(no != 0)
{
no = no / 10;
dig = dig + 1;
}
return dig;
}
// main method
public static void main(String argvs[])
{
// List for storing all the prime factors of a number
ArrayList<Integer> al = new ArrayList<Integer>();
for(int i = 1; i <= 30; i++)
{
findPrimeFactors(i, al);
int size = al.size();
int totalNoOfDig = findDigits(i);
if(size == totalNoOfDig)
{
System.out.println(i + " is an equidigital number.");    
}
else
{
System.out.println(i + " is not an equidigital number.");   
}
al.clear();
}
}
}

Output:

1 is not an equidigital number.
2 is an equidigital number.
3 is an equidigital number.
4 is not an equidigital number.
5 is an equidigital number.
6 is not an equidigital number.
7 is an equidigital number.
8 is not an equidigital number.
9 is not an equidigital number.
10 is an equidigital number.
11 is an equidigital number.
12 is not an equidigital number.
13 is an equidigital number.
14 is an equidigital number.
15 is an equidigital number.
16 is an equidigital number.
17 is an equidigital number.
18 is not an equidigital number.
19 is an equidigital number.
20 is not an equidigital number.
21 is an equidigital number.
22 is not an equidigital number.
23 is an equidigital number.
24 is not an equidigital number.
25 is an equidigital number.
26 is not an equidigital number.
27 is an equidigital number.
28 is not an equidigital number.
29 is an equidigital number.
30 is not an equidigital number.

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