Skip to main content

Dudeney Number

Dudeney number is a positive integer that is equal to the cube of the sum of all its digits.

Checking a Dudeney Number

Step 1: Consider any number.

Step 2: Sum all its digits.

Step 3: Cube the number obtained in Step 2.

If the number obtained in Step 3 is equal to the number considered in Step 1, it is a Dudeney number. But if the number obtained in Step 3 is not equal to the number considered in Step 1, it is not a Dudeney number.

Examples

Example 1

Step 1: Consider number 0.

Step 2: Sum all its digits. The resultant is 0.

Step 3: Cube the number 0 obtained in Step 2 => 03 => 0 x 0 x 0. The resultant is 0.

The number obtained in Step 3 is equal to the number considered in Step 1, hence 0 is a Dudeney number.

Example 2

Step 1: Consider number 1.

Step 2: Sum all its digits. The resultant is 1.

Step 3: Cube the number 1 obtained in Step 2 => 13 => 1 x 1 x 1. The resultant is 1.

The number obtained in Step 3 is equal to the number considered in Step 1, hence 1 is a Dudeney number.

Example 3

Step 1: Consider number 512.

Step 2: Sum all its digits (5 + 1 + 2). The resultant is 8.

Step 3: Cube the number 8 obtained in Step 2 => 83 => 8 x 8 x 8. The resultant is 512.

The number obtained in Step 3 is equal to the number considered in Step 1, hence 512 is a Dudeney number.

Example 4

Step 1: Consider number 4913.

Step 2: Sum all its digits (4 + 9 + 1 + 3). The resultant is 17.

Step 3: Cube the number 17 obtained in Step 2 => 173 => 17 x 17 x 17. The resultant is 4913.

The number obtained in Step 3 is equal to the number considered in Step 1, hence 4913 is a Dudeney number.

Example 5

Step 1: Consider number 5832.

Step 2: Sum all its digits (5 + 8 + 3 + 2). The resultant is 18.

Step 3: Cube the number 18 obtained in Step 2 => 183 => 18 x 18 x 18. The resultant is 5832.

The number obtained in Step 3 is equal to the number considered in Step 1, hence 5832 is a Dudeney number.

Example 6

Step 1: Consider number 17576.

Step 2: Sum all its digits (1 + 7 + 5 + 7 + 6). The resultant is 26.

Step 3: Cube the number 26 obtained in Step 2 => 263 => 26 x 26 x 26. The resultant is 17576.

The number obtained in Step 3 is equal to the number considered in Step 1, hence 17576 is a Dudeney number.

Example 7

Step 1: Consider number 19683.

Step 2: Sum all its digits (1 + 9 + 6 + 8 + 3). The resultant is 27.

Step 3: Cube the number 27 obtained in Step 2 => 273 => 27 x 27 x 27. The resultant is 19683.

The number obtained in Step 3 is equal to the number considered in Step 1, hence 19683 is a Dudeney number.

After considering the above examples, it is clear that the possible Dudeney numbers are: 0, 1, 512, 4913, 5832, 17576, and 19683.

Hope you liked this amazing concept of the Dudeney number. In case of any query, please feel free to provide your valuable comments.
Labels:

Comments

Post a Comment

Popular posts from this blog

Universe Secret Code 369 Theory

When it comes to the origin of the universe secret code 369 theory, one name associated with this amazing concept is ‘Nikola Tesla’. Nikola Tesla [10 July 1856 – 07 January 1943] was not only a great inventor / scientist, but also the greatest mind of all the time. He has done a plenty of research throughout his life, and highly recognized for his contributions towards the following : High Voltage, High Frequency Power Experiments Alternating Current (AC) Electricity Supply System Apart from the above-mentioned contributions, he has given ‘Universe Secret Code 369 Theory’ and has called the number 369 – the key to the universe. Now the question that will come to the curious minds is that why Nikola Tesla has called this number the key to the universe. The answer to this question is described in this post. Let start with a specific pattern as shown below: 1 1 + 1 => 2 2 + 2 => 4 4 + 4 => 8 8 + 8 => 16; 1 + 6 => 7 16 + 16 => 32; 3 + 2 => 5 >>>>>>...
Post a Comment
Read more

The RATS Sequence

In Mathematics, one of the amazing concepts is the Reverse-Add-Then-Sort (RATS) Sequence. The RATS Sequence is a sequence that is formed by reversing , adding , then sorting the digits. Let's understand this concept in detail: Form the RATS Sequence Step 1 : Consider any number (must be greater than 0). Step 2 : Reverse the number. Step 3 : Add the original number (considered in Step 1) with the number formed by reversing the number (in Step 2). Step 4 : Sort the number obtained in Step 3 in ascending order. The resultant obtained after sorting the number forms the next sequence after n iteration. Examples First Iteration Step 1 : Number 1 . Step 2 : Reversing the number 1  gives the resultant  1 . Step 3 : Adding the original number 1 (considered in Step 1) with the number formed by reversing (in Step 2)  i.e. 1 gives the resultant 2 . Step 4 : Sorting the number obtained in Step 3 in ascending order gives the resultant 2 . Here number 2 forms the next sequence after...
Post a Comment
Read more