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# 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**.

Letâ€™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:** Letâ€™s check another number **999** is smith or not.

Sum of digits = 9+ 9+9 = **27**

Prime factors of 999 is: 3Ã—3Ã—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. **27â‰ 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.

- If they are

Letâ€™s implement the above steps in a Java program.

## Smith Number Java Program

**SmithNumberExample1.java**

**Output 1:**

**Output 2:**

Letâ€™s create a Java program that finds all the smith numbers up to 10,000.

**SmithNumberExample2.java**

**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

#### Note: In the output above, we have shown only a few smith numbers because there are a lot of smith numbers. So, try it yourself.