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Thought-Process to Discover Knowledge

Welcome to **nub****trek**.

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

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

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.

Factors, Multiples, Prime Factorization

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

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.

The pages in this lesson are

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.

The pages in this lesson are

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`.

The pages in this lesson are

__Understanding Divisibility__ *redo *

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.

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.

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.