Divisible by 6
Divisible by 6 is discussed below:
Consider the multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, .........
All the multiples end with 2, 4, 6, 8 or 0.
Hence, these are divisible by 2.
|
Number |
Sum of the Digits |
|
12 18 24 48 54 |
1 + 2 = 3 1 + 8 = 9 2 + 4 = 6 4 + 8 = 12 5 + 4 = 9 |
Since the sums of the digits of all these multiples are divisible by 3, they are divisible by 3.
Numbers which are divisible by both 2 and 3 are divisible by 6.
1. Consider the following numbers which are divisible by 6, using the test of divisibility by 6: 42, 144, 180, 258, 156.
(i) 42
[We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].
42 is divisible by 2. Since the unit place is 2 which is divisible by 2.
[A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3].
42 is divisible by 3. Since the sum of the digits of 42 = 4 + 2 = 6 which is divisible by 3.
Therefore, 42 is divisible by both 2 and 3.
Hence, 42 is divisible by 6.
(ii) 144
[We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].
144 is divisible by 2. Since the unit place is 4 which is divisible by 2.
[A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3].
144 is divisible by 3. Since the sum of the digits of 144 = 1 + 4 + 4 = 9 which is divisible by 3.
Therefore, 144 is divisible by both 2 and 3.
Hence, 144 is divisible by 6.
(iii) 180
[We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].
180 is divisible by 2. Since the unit place is 0, divisible by 2.[A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3].
180 is divisible by 3. Since the sum of the digits of 180 = 1 + 8 + 0 = 9 which is divisible by 3.
Therefore, 180 is divisible by both 2 and 3.
Hence, 180 is divisible by 6.
(iv) 258
[We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].
258 is divisible by 2. Since the unit place is 8 which is divisible by 2.
[A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3].
258 is divisible by 3. Since the sum of the digits of 258 = 2 + 5 + 8 = 15 which is divisible by 3.
Therefore, 258 is divisible by both 2 and 3.
Hence, 258 is divisible by 6.
(v) 156
[We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].
156 is divisible by 2. Since the unit place is 6 which is divisible by 2.
[A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3].
156 is divisible by 3. Since the sum of the digits of 156 = 1 + 5 + 6 = 12 which is divisible by 3.
Therefore, 156 is divisible by both 2 and 3.
Hence, 156 is divisible by 6.
2. Consider the following numbers which are not divisible by 6, using the rules of divisibility by 6: 70, 135, 184, 286, 297.
Note: A number is divisible by 6 if it is divisible by 2 and 3 both.
(i) 70
[We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].
70 is divisible by 2. Since the unit place is 0 which is divisible by 2.
[A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3].
70 is not divisible by 3. Since the sum of the digits of 70 = 7 + 0 = 7 which is not divisible by 3.
Therefore, 70 is divisible by 2 but not by 3.
Hence, 70 is not divisible by 6.
(ii) 135
[We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].
135 is not divisible by 2. Since the unit place is 5, which is not divisible by 2.
[A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3].
135 is divisible by 3. Since the sum of the digits of 135 = 1 + 3 + 5 = 9 which is divisible by 3.
Therefore, 135 is divisible by both 3 but not by 2.
Hence, 135 is not divisible by 6.
(iii) 184
[We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].
184 is divisible by 2. Since the unit place is 4 which is divisible by 2.
[A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3].
184 is not divisible by 3. Since the sum of the digits of 184 = 1 + 8 + 4= 13 which is not divisible by 3.
Therefore, 184 is divisible by 2 but not by 3.
Hence, 184 is not divisible by 6.
(iv) 286
[We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].
286 is divisible by 2. Since the unit place is 6 which is divisible by 2.
[A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3].
286 is not divisible by 3. Since the sum of the digits of 286 = 2 + 8 + 6 = 16 which is not divisible by 3.
Therefore, 286 is divisible by 2 but not by 3.
Hence, 286 is not divisible by 6.
(v) 297
[We know the rules of divisibility by 2, if the unit’s place of the number is either 0 or multiple of 2].
297 is not divisible by 2. Since the unit place is 7, which is not divisible by 2.
[A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3].
297 is divisible by 3. Since the sum of the digits of 297 = 2 + 9 + 7 = 18 which is divisible by 3.
Therefore, 297 is divisible by both 3 but not by 2.
Hence, 297 is not divisible by 6.
3. Is 8622 divisible by 6?
The number ends in 2. Hence it is divisible by 2.
Sum of the digits = 8 + 6 + 2 + 2 = 18, is divisible by 3.
Hence 8622 is divisible by 6.
We can verify that 8622 is divisible by 6 by actual division.
Worksheet on Divisible by 6:
1. Which of the following numbers are divisible by 6?
(i) 258
(ii) 96420
(iii) 3448
(iv) 1360
(v) 4008
(vi) 771
(vii) 11190
(viii) 6124
Answer:
2. (ii) 96420
(v) 4008
(vii) 11190
You might like these
Highest Common Factor |Find the Highest Common Factor (H.C.F)|Examples
Highest common factor (H.C.F) of two or more numbers is the greatest number which divides each of them exactly. Now we will learn about the method of finding highest common factor (H.C.F). Steps 1: Find all the factors of each given number. Step 2: Find common factors of the
Prime Factorisation |Complete Factorisation |Tree Factorisation Method
Prime factorisation or complete factorisation of the given number is to express a given number as a product of prime factor. When a number is expressed as the product of its prime factors, it is called prime factorization. For example, 6 = 2 × 3. So 2 and 3 are prime factors
Multiples and Factors | Infinite Factors | Multiply Counting Numbers
We will discuss here about multiples and factors and how they are related to each other. Factors of a number are those numbers which can divide the number exactly. For example, 1, 2, 3 and 6 are
Divisible by 3 | Test of Divisibility by 3 |Rules of Divisibility by 3
A number is divisible by 3, if the sum of its all digits is a multiple of 3 or divisibility by 3. Consider the following numbers to find whether the numbers are divisible or not divisible by 3: (i) 54 Sum of all the digits of 54 = 5 + 4 = 9, which is divisible by 3.
Divisible by 4 | Test of Divisibility by 4 |Rules of Divisibility by 4
A number is divisible by 4 if the number is formed by its digits in ten’s place and unit’s place (i.e. the last two digits on its extreme right side) is divisible by 4. Consider the following numbers which are divisible by 4 or which are divisible by 4, using the test of
Divisible by 5 | Test of divisibility by 5| Rules of Divisibility by 5
Divisible by 5 is discussed below: A number is divisible by 5 if its units place is 0 or 5. Consider the following numbers which are divisible by 5, using the test of divisibility by
Divisible by 8 | Test of Divisibility by 8 |Rules of Divisibility by 8
Divisible by 8 is discussed below: A number is divisible by 8 if the numbers formed by the last three digits is divisible by 8. Consider the following numbers which are divisible by 8
Divisible by 7 | Test of Divisibility by 7 |Rules of Divisibility by 7
Divisible by 7 is discussed below: We need to double the last digit of the number and then subtract it from the remaining number. If the result is divisible by 7, then the original number will also be
Divisible by 9 | Test of Divisibility by 9 |Rules of Divisibility by 9
A number is divisible by 9, if the sum is a multiple of 9 or if the sum of its digits is divisible by 9. Consider the following numbers which are divisible by 9, using the test of divisibility by 9:
Divisible by 10|Test of Divisibility by 10|Rules of Divisibility by 10
Divisible by 10 is discussed below. A number is divisible by 10 if it has zero (0) in its units place. Consider the following numbers which are divisible by 10, using the test of divisibility by 10:
Least Common Multiple |Lowest Common Multiple|Smallest Common Multiple
The least common multiple (L.C.M.) of two or more numbers is the smallest number which can be exactly divided by each of the given number. The lowest common multiple or LCM of two or more numbers is the smallest of all common multiples.
Multiples | Multiples of a Number |Common Multiple|First Ten Multiples
What are multiples? ‘The product obtained on multiplying two or more whole numbers is called a multiple of that number or the numbers being multiplied.’ We know that when two numbers are multiplied the result is called the product or the multiple of given numbers.
Even and Odd Numbers Between 1 and 100 | Even and Odd Numbers|Examples
All the even and odd numbers between 1 and 100 are discussed here. What are the even numbers from 1 to 100? The even numbers from 1 to 100 are:
Prime and Composite Numbers | Prime Numbers | Composite Numbers
What are the prime and composite numbers? Prime numbers are those numbers which have only two factors 1 and the number itself. Composite numbers are those numbers which have more than two factors.
Worksheet on Divisibility Rules | Questions on Test of Divisibility
Worksheet on divisibility rules will help us to practice different types of questions on test of divisibility by 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11. We need to use the divisibility rules to find whether the given number is divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11.
Problems on Divisibility Rules
Worksheet on Divisibility Rules
5th Grade Math Problems
From Divisible by 6 to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
2nd Grade Geometry Worksheet | Plane and Solid Shapes | Point | Line
Dec 11, 24 09:08 AM
2nd grade geometry worksheet -
Types of Lines |Straight Lines|Curved Lines|Horizontal Lines| Vertical
Dec 09, 24 10:39 PM
What are the different types of lines? There are two different kinds of lines. (i) Straight line and (ii) Curved line. There are three different types of straight lines. (i) Horizontal lines, (ii) Ver… -
Points and Line Segment | Two Points in a Curved Surface | Curve Line
Dec 09, 24 01:08 AM
We will discuss here about points and line segment. We know when two lines meet we get a point. When two points on a plane surface are joined, a straight line segment is obtained. -
Solid Shapes | Basic Geometric Shapes | Common Solid Figures | Plane
Dec 08, 24 11:19 PM
We will discuss about basic solid shapes. We see a variety of solid objects in our surroundings. Solid objects have one or more shapes like the following. Match the objects with similar shape. -
2nd grade math Worksheets | Free Math Worksheets | By Grade and Topic
Dec 07, 24 03:38 PM
2nd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students.
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.