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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
6th-8th Foundation

Divisibility in Whole Numbers

When dividing a whole number, dividend, by another whole number, divisor, the result is quotient and remainder. The remainder is `0`, or in other words, the divisor divides the dividend without a remainder. This basic property leads to understanding all the following

 •  odd and even numbers

 •  prime and composite numbers

 •  factors and multiples of a number

 •  LCM and HCF

 •  Divisibility tests

This lesson provides breathtakingly simple and intuitive explanations to the above topics. Especially, the divisibility tests are explained in a simple-thought-process to understand why the procedure works.
(click for the list of lessons in this topic)

Classification of Numbers based on Remainder in Division: Odd-Even and Prime-Composite

This page introduces the following concepts in a simple thought process.

 •  The numbers that are divisible by `2` without a remainder, they are even. And the numbers that results in `1` as remainder, they are odd.

 •  Similarly prime numbers and composite numbers are defined.

(click for the list of pages in the lesson)

Factors, Multiples, Prime Factorization

Factors, Multiples, and Prime factorization are made simple and clear.

(click for the list of pages in the lesson)

Highest Common Factor

This lesson provides a brief overview of

 •  common factors

 •  highest common factor

 •  Simplified procedure to finding HCF

The above is explained in a simple-thought-process.

(click for the list of pages in the lesson)

Least Common Multiple

This lesson provides a brief overview of

 •  common multiples

 •  least common multiple

 •  Simplified procedure to finding LCM

 •  Relationship between the numbers, HCF, and LCM

The above is explained in a simple-thought-process.

(click for the list of pages in the lesson)

Basics of Divisibility Test

A number (dividend) is divisible by a divisor number if the remainder is `0`.

A procedure, to check if a given number is divisible by a divisor or not divisible by a divisor, is called divisibility test of the divisor. In this page, some basic divisibility tests for the following are introduced.

 •  product of multiple numbers

 •  sum of multiple numbers This forms the foundation to developing divisibility tests for numbers like `2, 3, 4, cdots`.

(click for the list of pages in the lesson)

Simple Divisibility Tests: 2, 10, 3, 4, 5, 11, 9, 6

In this page, a simple overview of the divisibility tests for `2, 10, 3, 4, 5, 11, 9, 6` are provided. The procedure is outlined with simple-reasoning, which helps students to understand the procedure.

(click for the list of pages in the lesson)

Simplification of Divisibility Tests: 8, 12, 15

To develop divisibility tests for numbers like `8, 12, 15`, the following methods of simplification are analyzed and explained.

 •  Simplification of divisibility test by subtraction

 •  Simplification of divisibility test by division

 •  Simplification of divisibility test by factors

Using the above, Divisibility tests for `8, 12, 15` are explained.

(click for the list of pages in the lesson)

Reducing number of Digits for Divisibility Test

To develop divisibility tests for numbers like `7` and `13`, "Simplification of divisibility test in number of digits" is analyzed and explained.

Using that, Divisibility tests for `8, 12, 15` are explained.

(click for the list of pages in the lesson)