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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.

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