nubtrek

Server Error

Server Not Reachable.

This may be due to your internet connection or the nubtrek server is offline.

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 division is explained. This is used to develop other divisibility tests for specific numbers.



click on the content to continue..

Given a number `340`. is it divisible by `21`?

Check this by long division method or by simplification by subtraction.

  • Yes
  • No
  • No
  • Can't say

The answer is "No". `340-210=130` and `130` is not divisible by `21`. So, the number is not divisible by `21`

Consider divisibility of `340` by `21`.

An observation is that the dividend is an even number and the divisor is not. The dividend can be written as `2xx170`.

Which of the following is true?

  • the divisibility test can be performed on `170` as the factor `2` is a co-prime of `21`
  • the divisibility test can be performed on `170` as the factor `2` is a co-prime of `21`
  • the divisibility test cannot be simplified

The answer is "the divisibility test can be performed on `170` as the factor `2` is co-prime of `21`".

This can further be simplified as `170-:2-:5 = 17`, as `2` and `5` are co-primes of `21`.

To check the divisibility of a composite dividend by a divisor, the factors of the dividend can help in simplifying the divisibility test.

 •  If a factor of dividend is co-prime of divisor, then the dividend can be divided by the co-prime factor and the divisibility test can be performed on the result.

This is named as Simplification by Division.

Simplification by Division: Dividend can be divided by a factor, that is co-prime of divisor, and the result is checked for divisibility.

Check divisibility of `990` by `13`

  • Divisible
  • Not Divisible
  • Not Divisible

The answer is "Not divisible". `10` and `9` are co-primes of `13`. So the number is divided as `990-:90 = 11`. The result `11` is not divisible by `13`.

                            
slide-show version coming soon