Tests for divisibility of numbers 2-4 — lesson. Mathematics State Board, Class 6.

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When a given number is divisible by another number without leaving a remainder, then the given number is said to be divisible of another number.

Divisibility rule gives a precise method to determine whether a given integer is divisible by a fixed divisor.

In this, we shall see the various types of divisibility. They are as follows:

Divisibility by $2$ .
Divisibility by $3$ .
Divisibility by $4$ .
Divisibility by $5$ .
Divisibility by $6$ .
Divisibility by $8$ .
Divisibility by $9$ .
Divisibility by $11$ .

Divisibility by

$2$ : If the number ends at

$2$ ,

$4$ ,

$6$ ,

$8$ or

$0$ , it is divisible by

$2$ .

Example:

1. Let us take the numbers

$28$ ,

$54$ ,

$96$ .

Rule for

$2$ : Number ends at

$2$ ,

$4$ ,

$6$ ,

$8$ or

$0$ .

Here

$28$ ,

$54$ , and

$96$ ends with

$8$ ,

$4$ , and

$6$ respectively.

Hence,

$28$ ,

$54$ and

$96$ are divisible by

$2$ .

2. Let us take the numbers

$35$ ,

$57$ ,

$1297$ .

Rule for

$2$ : Number ends at

$2$ ,

$4$ ,

$6$ ,

$8$ or

$0$ .

Here

$35$ ,

$57$ ,

$1291$ ends with

$5$ ,

$7$ , and

$1$ respectively.

Hence,

$28$ ,

$54$ and

$96$ are not divisible by

$2$ .

Divisibility by

$3$ : If the sum of its digits of any number is divisible by

$3$ then that number is divisible by

$3$ .

Example:

1. Let us take the number

$429$ .

Rule for

$3$ : Sum of the digits of the number is divisible by

$3$ .

$4+2+9=15$ ;

$15\div3=5$

Hence,

$429$ is divisible by

$3$ .

2. Let us take the number

$512$ .

Rule for

$3$ : Sum of the digits of the number is divisible by

$3$ .

$5+1+2$

$=$

$8\div3$ . This division leaves a remainder

$2$ .

Hence,

$512$ is not divisible by

$3$ .

Divisibility by

$4$ : If a last two digits of any number are divisible by

$4$ , then that number is divisible by

$4$ .

Example:

1. Let us look at the number

$628$ .

Rule for

$4$ : Last

$2$ digits of the number is divisible by

$4$ .

Last

$2$ digits are

$28$ and

$28\div4=7$ .

Hence,

$628$ is divisible by

$4$ .

2. Let us look at the number

$714$ .

Rule for

$4$ : Last

$2$ digits of the number is divisible by

$4$ .

Last

$2$ digits are

$14$ and

$14\div4$ . This division leaves a remainder

$2$ .

Hence,

$714$ is not divisible by

$4$ .

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1. Tests for divisibility of numbers 2-4

Theory: