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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, Simplification of divisibility test by subtraction is explained. This is used to develop other divisibility tests for specific numbers.



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Given a number `83xx2322 = 192726`. is it divisible by `83`?

  • Yes
  • Yes
  • No
  • Can't say

The answer is "Yes". The number is given as a multiple of `83`, so it is divisible by `83`.

Consider a number `83xx23 + 422 = 2331`, Which of the following helps to find if the number is divisible by `83`?

  • we have to check the large number `2331`
  • we can check the smaller number `422` which is easier
  • we can check the smaller number `422` which is easier

The answer is "we can check the smaller number `422` which is easier".

Consider a number `2331`, Which of the following helps to find if it is divisible by `83`?

  • we have to check the large number `2331`
  • it can be simplified to a smaller number `2331-83xx20=671` which is easier
  • it can be simplified to a smaller number `2331-83xx20=671` which is easier

The answer is "It can be simplified to a smaller number".

To check the divisibility, the following properties are helpful.

 •  multiple of a number is divisible by the number.
eg: `3xx423` is a multiple of `3` and so it is divisible by `3`.

 •  In a sum of two numbers, if one number is a multiple of the divisor, then only the other number is checked for divisibility.
eg: Divisibility test of `3xx423 + 7` by `3`, can be simplified to divisibility test of `7`, as `3xx423` is a multiple of `3`.

 •  To check divisibility of a large number by a divisor, it can be simplified into a smaller number by subtracting a multiple of the divisor.
eg: Divisibility test of `913` by `3`, can be simplified to divisibility test of `913-300xx3 = 13`

The method is named Simplification by Subtraction method.

Simplification by Subtraction for Divisibility Tests: To perform divisibility test on a large number, a multiple of a divisor can be subtracted and the divisibility test is performed on the difference.

Find the divisibility of `777012` by `111`.

  • Not Divisible. Subtract `777012 - 111xx7000 = 12`. Check the divisibility on `12`
  • Not Divisible. Subtract `777012 - 111xx7000 = 12`. Check the divisibility on `12`
  • It is not simple to check divisibility large numbers

The answer is "Not Divisible"

Find the divisibility of `804` by `67`.

  • Not Divisible. Subtract `804 - 67xx10 = 134`. Check the divisibility on `134`
  • Divisible. `134=67xx2` is divisible by `67`
  • Divisible. `134=67xx2` is divisible by `67`

The answer is "Divisible"

                            
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