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.

Divisibility of a Number

In this page, the concept of divisibility is introduced with simple examples. Then odd and even numbers are introduced. Then prime and composite numbers are explained.

Factors, Multiples, Prime Factorization

This page provides a brief overview of
*factors of a number*.
*multiplies of a number*.
*prime factorization of numbers*

Common Factors & HCF

This page provides a brief overview of

*common factors of two or more numbers*,

*co-prime numbers*,

*highest common factor of two or more numbers*,

*highest common factor using factorization method*,

*highest common factor using division method*

Common Multiples & LCM

This page provides a brief overview of

*common multiples of two or more numbers*,

*lowest common multiple of two or more numbers*,

*least common multiple using factorization method*,

*product of numbers equals product of their LCM and HCF*

Introduction to Divisibility Tests

This page

• provides basics required to understand what is a divisibility test.

• analyses developing divisibility test procedure for numbers given as product of multiple numbers. This forms the foundation to developing other divisibility tests for specific numbers.

• develops divisibility test procedure for numbers given as sum of multiple numbers. This forms the foundation to developing other divisibility tests for specific numbers.

Simple Divisibility Tests

In this page, simple divisibility tests for $2$, $10$, $3$, $4$, $5$, $11$, $9$, $6$ are explained.

Simplification of Divisibility Tests

In this page, methods to simplify divisibility tests are explained.

• Simplification of divisibility test by subtraction

• Simplification of divisibility test by division

• Simplification of divisibility test by factors

These are used to develop other divisibility tests for specific numbers.

• the divisibility test for $8$

• the divisibility test for $12$

• the divisibility test for $15$

Simplification of Digits for Divisibility Tests

In this page, Simplification of Divisibility test, by reducing the number of digits of the dividend, is explained. This method is used to derive divisibility tests for $7$ and $13$.