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.
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 2 Video |Test of Divisibility by 2 Trick| Rules| Examples
A number is divisible by 2 if the digit at unit place is either 0 or multiple of 2. So a number is divisible by 2 if digit at its units place is 0, 2, 4, 6 or 8.
Divisible by 3 | Test of Divisibility by 3 Trick | Rules | Video
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 Trick | Rules | Video
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 | Rules for Test of divisibility by 5 | Video |Examples
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 | Video | Examples
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 Video | Rules | Examples
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.
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
-
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 -
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 -
Expanded form of Decimal Fractions |How to Write a Decimal in Expanded
Apr 17, 25 12:21 PM
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… -
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… -
Place Value and Face Value | Place and Face Value of Larger Number
Apr 16, 25 02:55 PM
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…
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.