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What are The Multiples of 6?

What is Multiplication?

Last updated date: 30th Jan 2023
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Multiplication is defined as the process of repeatedly adding a number to another number in mathematics. When we multiply 2 by 4, for example, we are adding 4 to itself twice, giving in 4 + 4 = 8. This is a simple approach for children to multiply numbers.


Here are a few more examples:

  • 3 by 6 = 3 + 3 + 3 + 3 + 3 + 3 = 18

  • 4 by 5 = 4 + 4 + 4 + 4 + 4= 20

  • 5 by 9 = 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 45

The task of multiplying single-digit values is simple. Multiplying two or more digit numbers, on the other hand, can be complicated and time-consuming.


Symbol

The method of multiplication is denoted by a cross sign (×) and sometimes by a dot (.).

Examples:

  • 3 × 12 = 36

  • 5 × 6 = 30

  • 8 × 2 × 6 = 96

  • (9).(9) = 81

  • (5).(8) = 40


Properties of Multiplication

The properties of multiplication are given as,


Multiples of 6

The products of 6 and natural integers are known as multiples of 6. Look at it another way, a multiple of 6 is a number that can be divided by 6 with no remainder. Multiples of 6 have a difference of 6 between them, which is interesting. We'll calculate the multiples of 6 and learn some fascinating facts about them in this mini-lesson. Let's study more about multiples of 6 in tabular form with examples in this article.

  • First, 6 multiples of 6 are 6, 12, 18, 24, 30, and 36.

  • Prime factorizations of 6 are 2 x 3


What are The Multiples of 6?

The product of 6 with any natural number is a multiple of 6. The numbers that are formed when 6 is multiplied by any natural number, such as 1, 2, 3, 4, 5, 6, 7, and so on, are known as 6 multiples. That is, any number that can be written as 6n, where n is an integer, is a multiple of 6. We say that q is a multiple of p if q = np for some number n if two values, p and q, are given. Many of the multiples of 6 include the following.

6, 12, 18,.…., 54, 60,.…, 90, 96,..…

According to the definition, a multiple of 6 is obtained by multiplying an integer by 6. For the following reasons, 48, 72, 114, and 132 are all multiples of 6.


6 × 8 = 48

6 multiplied by 8 to get 48

6 × 12 = 72

6 multiplied by 12 to get 72

6 × 19 = 114

6 multiplied by 19 to get 114

6 × 22 = 132

6 multiplied by 22 to get 132


We can also find the multiples by adding a number to itself as many times as required. For example, multiply 6 by 1, 2, 3, 4, and 5 or add the number of times as indicated below to get the first five multiples of 6:

  • The first multiple of 6 is: 6 × 1 = 6

  • The 2nd multiple of 6 is 12: 6 + 6 = 12 Or 6 × 2 = 12 {here 6 is added for twice}

  • The 3rd multiple of 6 is 18: 6 + 6 + 6 = 18 Or 6 × 3 = 18 {here 6 is added for thrice}

  • The 4th multiple of 6 is: 6 + 6 + 6 + 6 Or 6 × 4 = 24 = 24

  • The 5th multiple of 6 is: 6 + 6 + 6 + 6 + 6 Or 6 × 5 = 30 = 30

Similarly, we calculate several multiples of the given numbers.


Multiples of 6 and 9 Table

The following table contains the first 20 multiples of 6 and 9 along with the multiplication notation in each case.


Multiplication of 6 with numbers

Multiples of 6

Multiplication of 9 with numbers

Multiples of 9

6 × 1

6

9 × 1

9

6 × 2

12

9 × 2

18

6 × 3

18

9 × 3

27

6 × 4

24

9 × 4

36

6 × 5

30

9 × 5

45

6 × 6

36

9 × 6

54

6 × 7

42

9 × 7

63

6 × 8

48

9 × 8

72

6 × 9

54

9 × 9

81

6 × 10

60

9 × 10

90

6 × 11

66

9 × 11

99

6 × 12

72

9 × 12

108

6 × 13

78

9 × 13

117

6 × 14

84

9 × 14

126

6 × 15

90

9 × 15

135

6 × 16

96

9 × 16

144

6 × 17

102

9 × 17

153

6 × 18

108

9 × 18

162

6 × 19

114

9 × 19

171

6 × 20

120

9 × 20

180


From the above table, we can say that the multiples of the numbers 6 and 9 are the results in the multiplication table of 6, as both are the same.


What is The Difference Between a Multiple and a Factor of 6?

Multiples are the n-times of every given integer, as we've already discussed. Factors, on the other hand, are the numbers that, when multiplied together, produce the original number. Any number's multiples can be extended forever, but the factors are constant for all numbers.


How Many Multiples of 6 are in Between 1 to 100?

As we know there are infinite multiples of 6 but here are all multiples of 6 which lie between 6 to 100,

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, and 96.


Solved Examples

1. Aadhya started to make bracelets in such a way that the first bracelet includes 6 beads, the second one had 12, the third one has 18 and continued. What is the number of beads that she needs to make the 25th bracelet?

Ans: From the given data the number of beads in each bracelet had increased, i.e 6, 12, 18…..

Hence by the sequence, we can conclude that it represents the multiple of ‘6’.

Therefore, the number of beads required in the 25th bracelet will be 25 multiplied by 6, hence the final answer is 150.


2. Mikhael gets 6 coins for every jump he makes in a video game, after some time he has finished his game by 112 jumps. Now find the number of coins he collected at the end of the game.

Ans: From the given data we can conclude that for every jump he receives 6 points hence the total coins collected will be the multiple of 6. Thus for 112 jumps the total coins collected will be 112 multiplied by 6.

Hence the final answer will be 672 coins.


Practise Questions

1. Sheela has calculated that the 68th multiple of 6 and the value will be 408. Now help her to calculate the 69th multiple?

  1. 414

  2. 412

  3. 416

  4. 418

Ans: Option a


2. Sara writes a sequence where they are multiples of 6 and concludes that all the multiples are written are multiples of both 2 and 3.

  1. True

  2. False

Ans: Option a


Facts

  • The zero property of multiplication states that whenever there is a zero in a given problem, the final answer will be zero.

  • In the case of 9’s multiplication, the sum of 10’s and 1’s digit will always end up y 9.

  • Multiplication obeys both commutative and associative properties.

  • The inverse process of multiplication is division.


Conclusion

The product of any two integers leads to a specific number this process is generally called multiplication. The multiples of any number can be infinite whereas the multiplication of two numbers is finite. Even the outcome will be greater than those two numbers.

FAQs on What are The Multiples of 6?

1. What are the common multiples of 6 and 4?

Multiples of 6 are 6, 12, 18, 24, 30, 36, … and Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, …  So, the common multiples of 6 and 4 are 12, 24, 36, …

2. What are the factors 6?

Factors of 6 are as given below,

  • Factors of 6: 1, 2, 3 and 6.

  • Negative Factors of 6: -1, -2, -3 and -6.

  • Prime Factors of 6: 2, 3.

  • Prime Factorization of 6: 2 × 3 = 2 × 3.

  • Sum of Factors of 6: 12.

3. Are multiples of 3 always multiples of 6?

No. By noticing that every multiple of 3 is a multiple of 6, we will see that all multiples of 6 are also multiples of 3 because 3 is a factor of 6 except 9. After all, 9 is a multiple of 3 but not 6. Hence every multiple of 3 is not always multiple of 6.

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