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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.

In this page, a simple overview of the divisibility test for 7 is provided. The procedure uses simplification in Digits.

click on the content to continue..

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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