In this article, we are going to learn to find `Magic Number`

using Java.

Table of Contents

## What is a Magic Number?

A number which leaves 1 as a result after a sequence of steps and in each step number is replaced by the sum of its digits. For example, if we check whether 163 is a Magic Number, then sequence of steps are

`Step 1:`

1+6+3 = 10 **// Sum of square of each digit**

`Step 2:`

1+0 = 1 (A Magic Number)

To calculate magic number, we have two approaches either using recursive approach or simple a shorthand logic. Let’s see the examples.

**Algorithm for Magic Number**

`Step 1:`

Take two variables, `sum`

for storing a sum of square and `number`

for holding the value.

`Step 2:`

Repeat till `number`

greater than 0 or `sum`

is greater than 9.

`Step 3:`

If `number`

is equal to 0, replace the number with the `sum`

of the digits and set `sum`

= 0.

`Step 4:`

Calculate the `sum`

of each digit present in the `number`

and add it to the variable `sum`

.

`Step 5:`

If result `sum`

is equal to 1, then the `number`

is a Magic Number.

`Step 6:`

Else the `number`

is not Magic Number.

## Example to find Magic Number

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public class Main{ public static void main(String[] args) { int number = 1000; // Number to check int sum = 0; while (number > 0 || sum > 9) { if (number == 0) { number = sum; sum = 0; } sum += number % 10; number /= 10; } // If sum = 1, it is magic number if(sum == 1) { System.out.println("It is a magic number"); }else { System.out.println("It is not a magic number"); } } } |

Output:

## Another Example To find Magic Number

There is another approach to find Magic Number. In this approach, we can get Magic Number after dividing a number by 9. This is a shortcut method to verify Magic Number. If we get remainder 1 after dividing a number by 9 then the number is a magic number. It is based on the concept of divisibility rule of 9 which says that if a number is divisible by 9, then sum of its all digits are also divisible by 9. An addition of 1 in the original number will increase the ultimate value by 1, making it 10 and the ultimate sum will be 1, which makes a number a magic number. See the example below.

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public class Main{ public static void main(String[] args) { int number = 10001; // Number to check if(number % 9 == 1) { System.out.println("It is a magic number"); }else { System.out.println("It is not a magic number"); } } } |

Output

That’s all about magic number in java.