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.

Divisibility Rule for 6 Video

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. Subtraction of Decimals | Subtracting Decimals | Decimal Subtraction

    Apr 17, 25 01:54 PM

    We will discuss here about the subtraction of decimals. Decimals are subtracted in the same way as we subtract ordinary numbers. We arrange the digits in columns

    Read More

  2. Addition of Decimals | How to Add Decimals? | Adding Decimals|Addition

    Apr 17, 25 01:17 PM

    We will discuss here about the addition of decimals. Decimals are added in the same way as we add ordinary numbers. We arrange the digits in columns and then add as required. Let us consider some

    Read More

  3. Expanded form of Decimal Fractions |How to Write a Decimal in Expanded

    Apr 17, 25 12:21 PM

    Expanded form of Decimal
    Decimal numbers can be expressed in expanded form using the place-value chart. In expanded form of decimal fractions we will learn how to read and write the decimal numbers. Note: When a decimal is mi…

    Read More

  4. Math Place Value | Place Value | Place Value Chart | Ones and Tens

    Apr 16, 25 03:10 PM

    0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are one-digit numbers. Numbers from 10 to 99 are two-digit numbers. Let us look at the digit 6 in the number 64. It is in the tens place of the number. 6 tens = 60 So…

    Read More

  5. Place Value and Face Value | Place and Face Value of Larger Number

    Apr 16, 25 02:55 PM

    Place Value of 3-Digit Numbers
    The place value of a digit in a number is the value it holds to be at the place in the number. We know about the place value and face value of a digit and we will learn about it in details. We know th…

    Read More