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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 `7` is provided. The procedure uses simplification in Digits.



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Which of the following helps in divisibility test of `7`?

  • simplification in digits as `7xx3=21`
  • simplification in digits as `7xx3=21`
  • divisibility test cannot be simplified for `7`

The answer is "simplification in digits as `7xx3=21`".

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

then the number can be modified to `10A+B-21B` (simplification by subtraction)

which equals ` 10A-20B=10xx(A-2B)`.

Since `7` is co-prime to both `2` and `5`, the divisibility test is done on `A-2B` (simplification by division). This, in effect, reduced the number of digits in `10A+B`.

Note: `A-2B` can further be simplified using the same procedure.

Test for Divisibility by `7` : Reduce the number of digits by iteration.

Remove the units digit from the number to get a modified number. Subtract double of the removed digit in units place from the modified number.

Perform the divisibility test on the difference.

Is `2008` divisible by `7`?

  • Yes
  • No
  • No

The answer is "No". Following the process

`2008`
`->200-2xx8`
`->184`
`->18-2xx4`
`->10`

`10` is not divisible by `7`, and so it is concluded that the number is not divisible by `7`.

Is `406` divisible by `7`?

  • Yes
  • Yes
  • No

The answer is "Yes". Following the process

`406`
`->40-2xx6`
`->28`

`28` is divisible by `7`, and so it is concluded that the number is divisible by `7`.

                            
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