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.


Divisible by 6


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

 Divisibility Rules.

Properties of Divisibility.

Divisible by 2.

Divisible by 3.

Divisible by 4.

Divisible by 5.

Divisible by 6.

Divisible by 7.

Divisible by 8.

Divisible by 9.

Divisible by 10.

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.



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.

Share this page: What’s this?

Recent Articles

  1. Worksheet on Triangle | Homework on Triangle | Different types|Answers

    Jun 21, 24 02:19 AM

    Find the Number of Triangles
    In the worksheet on triangle we will solve 12 different types of questions. 1. Take three non - collinear points L, M, N. Join LM, MN and NL. What figure do you get? Name: (a)The side opposite to ∠L…

    Read More

  2. Worksheet on Circle |Homework on Circle |Questions on Circle |Problems

    Jun 21, 24 01:59 AM

    Circle
    In worksheet on circle we will solve 10 different types of question in circle. 1. The following figure shows a circle with centre O and some line segments drawn in it. Classify the line segments as ra…

    Read More

  3. Circle Math | Parts of a Circle | Terms Related to the Circle | Symbol

    Jun 21, 24 01:30 AM

    Circle using a Compass
    In circle math the terms related to the circle are discussed here. A circle is such a closed curve whose every point is equidistant from a fixed point called its centre. The symbol of circle is O. We…

    Read More

  4. Circle | Interior and Exterior of a Circle | Radius|Problems on Circle

    Jun 21, 24 01:00 AM

    Semi-circular Region
    A circle is the set of all those point in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is known

    Read More

  5. Quadrilateral Worksheet |Different Types of Questions in Quadrilateral

    Jun 19, 24 09:49 AM

    In math practice test on quadrilateral worksheet we will practice different types of questions in quadrilateral. Students can practice the questions of quadrilateral worksheet before the examinations

    Read More