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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.
mathsDivisibility in Whole NumbersSimplification of Divisibility Tests: 8, 12, 15

### Divisibility: Simplification by Division

In this page, Simplification of divisibility test by division is explained. This is used to develop other divisibility tests for specific numbers.

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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.

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