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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue

In this page, a simple overview of the divisibility test for `13` is provided. The procedure uses simplification in Digits.



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Which of the following helps in divisibility test of `13`?

  • simplification in digits as `13xx3=39`
  • simplification in digits as `13xx3=39`
  • divisibility test cannot be simplified for `13`

The answer is "simplification in digits as `13xx3=39`".

If the given dividend is `10A+B`, (where `B` is a single digit number)

then the dividend can be modified to `10A+B+39B` (simplification by addition)

which equals `10A+40B = 10(A+4B)`.

Since `13` is co-prime to both `2` and `5`, the divisibility test is done on `A+4B` (simplification by division). This, in effect, reduced the number of digits in `10A+B`.

Note: `A+4B` can further be simplified using the same procedure.

Test for Divisibility by `13` : Reduce the number of digits by iteration.

Remove the units digit from the dividend to get a modified number. Add `4` times of the removed units digit to the modified number.

Perform the divisibility test on the sum.

Is `2008` divisible by `13`?

  • Yes
  • No
  • No

The answer is "No". Following the process

`2008`
`->200+4xx8`
`->232`
`->23+4xx2`
`->31`

`31` is not divisible by `13`, and so it is concluded that the number is not divisible by `13`.

Is `416` divisible by `13`?

  • Yes
  • Yes
  • No

The answer is "Yes". Following the process

`416`
`->41+4xx6`
`->65`
`->6+4xx5`
`->26`

`26` is divisible by `13`, and so it is concluded that the number is divisible by `13`.

                            
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