**Contents**show

## What is meant by Smith number?

A Smith number is **a composite number, the sum of whose digits equals the sum of the digits of all its prime factors**. The smallest Smith number is 4 = 2×2. The sum of the digits of 4 is 4, and The sum of digits of its prime factors is 2 + 2 = 4.

## What is the logic of Smith number?

In number theory, a Smith number is a composite number for which, in a given number base, **the sum of its digits is equal to the sum of the digits in its prime factorization in the given number base**.

## What is a magic number in Java example?

**If the single digit is 1 then** the number is called a magic number. It is quite similar to the happy number. For example, 325 is a magic number because the sum of its digits (3+2+5) is 10, and again sum up the resultant (1+0), we get a single digit (1) as the result. Hence, the number 325 is a magic number.

## Is 11 a Smith number?

The first few Smith numbers are 4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, … (OEIS A006753). The corresponding digits sums are 4, 4, 9, 13, 13, 13, 4, 13, 4, 13, 13, 13, 13, …

## What is the perfect number?

Perfect number, **a positive integer that is equal to the sum of its proper divisors**. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128. The discovery of such numbers is lost in prehistory.

## Is 5 an Automorphic number?

An automorphic number is a number whose square ends with the number itself. For example, 5 is an automorphic number, **5*5 =25**. The last digit is 5 which same as the given number. It has only a positive single digit number.

## How do I find my Smith number?

**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.

## Is Armstrong a number?

Armstrong number is **a number that is equal to the sum of cubes of its digits**. For example 0, 1, 153, 370, 371 and 407 are the Armstrong numbers.

## Is 197 a Keith number?

, … (Keith). Keith numbers are also called repfigit (repetitive fibonacci-like digit) numbers.

…

Keith Number.

-digit Keith numbers | |
---|---|

3 | 197, 742 |

4 | 1104, 1537, 2208, 2580, 3684, 4788, 7385, 7647, 7909 |

5 | 31331, 34285, 34348, 55604, 62662, 86935, 93993 |