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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 13 is provided. The procedure uses simplification in Digits.

click on the content to continue..

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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