# data[].attributes.body
Knowing that 6 is an even number, any multiple of 6 is definitely a multiple of 2.

Also, 6 can be divided by 3 so 3 is definitely a multiple of any multiple of 6.

Thus concluding that 2 and 3 are multiple of any multiple of 6.

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1. Answer each question in a new post, indicate "Question number" in the title
2. Post your answer to each question in a new post

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If 2 and 3 are factors of a number, then 6 is also a factor of that number?

If it is TRUE: Illustrate why it is true (you may give some examples)

If it is FALSE: Give a counter-example

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If 6 is a multiple of a number, then 12 is also multiple of that number?

If it is TRUE: Illustrate why it is true (you may give some examples)

If it is FALSE: Give a counter-example

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Is it true that...
If 6 is a a factor of a number, then 2 and 3 are also factors of that number?

Answer:
It is TRUE because...
e.g. 6 is a factor of the number 30
6 x 5 gives 30
Since 6 = 2 x 3, we can write
(2 x 3) x 5 = 30, which means 2 and 3 are factors of 30, too

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Yes
Since 2and3are factors of 6

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For example 3,2and6 are all factors of 12

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Yes since they are both multiples of 6

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It is true.
2×3=6
Examples:
2×12=24
3×8=24
6×4=24

2×6=12
3×4=12
6×2=12

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Q1: True
6 is a factor of 6, 12, 18, 24 etc.

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It is true.

6 is a multiple of:
1, 2, 3, 6

12 is a multiple of:
1, 2, 3, 4, 6, 12

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True:

2 x 3 = 6

Meaning that 2 and 3 are factors of 6.
All multiples of 6 will have the same factors of 6. 2 and 3 are also prime factors.
For example:
The factors of 12 are
1 x 12
2 x 6
3 x 4

The numbers 2 ,3 and 6 are all factors of 12

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True:
The multiples of 6 are:
1 (1x6), 2 (2x3), 3 (3x2), 6 (6x1)

The multiples of 12 are:
1 (1x12), 2 (2x6), 3 (3x4), 4 (4x3), 6 (6x2), 12 (12x1)

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It is true
As 2 x 3 = 6
and 3 x 2 = 6
And 6 can still be a factor of 6 as 1 x 6 is 6

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It is true.

For example the number 36.

6 is a factor of 36 as 36 is divisible by 6.
In that case, the prime numbers that make up 6 in index notation is 2x3. Thus, with this concept, if we divide 36 using 2 and 3, we can get a whole number, inferring that 2 and 3 are factors of 36.

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It is false as it is not always true.

Example:

Let's use 24 as an example. 24/12= 2. This makes 24 BOTH a multiple of 6 and 12.

However, I believe that there are exceptions. Let's take an example a number that is a multiple of 6, like 30.
6x5 = 30

If 30/12, we will get a decimal, and not a whole number, proving that 12 is NOT a multiple of 30 ALTHOUGH 30 is a multiple of 6.

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2x12 is 24 which can also be divided by 6 so can 2x9 and 2x6
3x4,3x6,3x8 all can be divided by 6

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It is false.
For example take 18, 6 is a multiple of 18 but 12 is not as it is 12,24 and not 18

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It is true
e.g. The lowest number that 2 and 3 are factors of is 12, which also has 6 as a factor. Which means that any number that has factors that include 2 and 3 will also have 6 as its factor

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It is true as 6 has factors of 1,2,3,6 and 12 has factors of 1,2,3,6 too so whatever is a multiple of six will definitely have the same factors of 6

# data[].attributes.subject
It is true as 6 has factors of 1,2,3,6 and 12 has factors of 1,2,3,6 too so whatever is a multiple of six will definitely have the same factors of 6

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When 6 is multiplied by an odd number, example like 7, 6X7 equals 42, which is not a multiple of 12

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If 2 and 3 are factors of a number, for example, 12, 6 will also be a factor
2x3=6
1x6=6

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For example, 12 is a multiple of 3, and 6 is also a multiple of 3, and 6x2=12

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The numbers such as 6, 18 and 30 are not multiples of 12 although they are multiples of 6, thus concluding that not all multiples of 6 are multiples of 12.

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It is true because 6 is a bigger number than 2 and 3 and therefore, knowing that 2 and 3 are factors of 6, any number which is a multiple of 6 will definitely be a multiple of 2 and 3.

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True.
12 factors: 1,2,3,4,6,12
18 factors: 1,2,3,6,9,18
36 factors: 1,2,3,4,6,9,12,18,36
The three numbers above are divisible by 6 and also by 2 and 3 which are both factors of 6.

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True
2 and 3 are factors of 6
6 is also 6's factor

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True.
6's factors: 1,2,3,6
12's factors: 1,2,3,4,6,12
Since 6 has the same factors has 12, a multiple of any of 6's factors would also be a have a multiple of 12.

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Because 2 and 3 are factors of 6

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True
3,6,9,12
6,12

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Q1. It is true
2 and 3 are both factors of 6 and 6 can be represented as 2x3.
thus, if 2 and 3 are both factors of a number, 6 will also be a factor since 2x3=6.
e.g. 2 and 3 are factors of 12
6 is also a factor of 12

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12 is not a factor of 6

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Q2. It is true
6 is a multiple of 1,2,3 and 6
12 is also a multiple of 1,2,3 and 6

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Yes.
Because 2 multiplied by 3 is 6.
Let us suppose that the number that the teacher was talking about is x:
If x = 12: 1, 2, 3, 4, 6, 12
If x = 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
As you can see 2, 3 and 6 are all factors of x.
I rest my case.

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Yes.
Because 6 is a factor of 12.
Let us suppose that the number that the teacher was talking about is x:
If x = 1 then 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
If x = 3 then 3, 6, 9, 12
As you can see 6 and 12 are all multipliers of x.
I rest my case.

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Question 1: True
As 2 and 3 are prime numbers, and 2*3=6, if 2&3 are factors of a number, 6 is also a factor.

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Question 2: True
12 is a multiple of 6, so if 6 is a multiple of a certain number, 12 will also be a multiple.

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12
2x6=12
3x4=12
<>
6x2=12

24
2x12=24
3x8=24
<>
6x4=24

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because 6 is half of 12.
e.g.
3,6,9,12
^     ^
2,4,6,8,10,12
^ ^

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as long as 2 and 3 are factors of a number, 6 will also be a factor of that number as 2x3=6
lets say the number is 48.
48 can be divided by 3,
48 can be divided by 2,
and 48 can be divided by 6.

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True,
Because 2 x 3 = 6.
6 is also a factor of 6

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Since 6 is half of 12, it can be a multiple of the number in between every multiple of 12.
for example, 24 and 36 is a multiple of 12.
since 6 is half of 12, it can be a multiple of 30 while 12 cant.

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False,
Because for example: 30
30 is a multiple of 6, but not a multiple of 12.
There are some numbers that are both multiples of 6 and 12 though.

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Approximately slightly more than half of the multiples of 3 can be divided by 6.

However, all even multiples of 3 can be divided by 6. This is because the first multiple of 3 that is even is 6.

As all even numbers share a common factor, 2, all numbers with both 3 and 2 as factors are dividable by 6.

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The factors of 6 are:
1,2,3,6
6 is a multiple of the above numbers.

The factors of 12 are:
1,2,3,4,6,12
12 is a multiple of the above numbers.

12 is a multiple of all the numbers 6 is a multiple of.

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The smallest number with 2 and 3 as factors is 6 meaning all other numbers following the same rule will have 6 as a factor as well

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12 is a multiple of 6 meaning that 12 would also be a multiple of that number

e.g. --> 2*3=6
2*6=12

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True.

When you use a factor tree, you can see that 6 is equal to 2 times 3, so any multiple of 6 is also a multiple of 2 and 3.

Examples: 12= 2x6
= 2x3x2

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False.

If 12 is a multiple of a number then 6 also is, but not neccesarily the other way round.

Example: 3 x 6 = 18
18 divided by 12 = ❌

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Question 1: Yes, it is true
2 and 3 are factors of 6.
6 is an even number so it’s  multiples are also even
Example: 6,12,18 (2 is also an even number so all the multiples of 6 will also be multiples of 2)
6 divided by 3 is 2. So for the 2nd, 4th, 6th, multiples of 3 and so on, are also multiples of 6
Example: 3,     6,    9,    12
Odd   —  Odd  —
So if a number has 2 and 3 as two of its factors, it would have 6 as one of its factors.

# data[].attributes.body
It is true.
The factors of 6 are 1, 2, 3 and 6. As you can see, 2 and 3 are factors of 6.
That means that whichever number 2 and 3 are factors of, 6 will also be a factor of that number.
An example:
2 x 9 = 18
3 x 6 = 18
As shown, 6 is a factor of 18 while 2 and 3 are as well.
The same idea applies to other numbers like 24 and 36.

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Question 2: Yes, it is true.

Factors of 6:    1,2,3,6

12 divided by 1 = 12
12 divided by 2 = 6
12 divided by 3 =4
12 divided by 6 =2
All the answers are while numbers so hence, it is true.

Multiples of:
1:  1,2,3,4,5,6,7,8,9,10,11,12
2:  2,4,6,8,10,12
3:  3,6,9,12
6: 6,12

# data[].attributes.body
It depends on which number.

If you take 18 for example, although 6 is a factor of that number, 12 isn't.

However, if you take 36, both 12 and 6 are factors of that number.

So it entirely depends on which number you are using.

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Q1: It is true. For example, the number 18 has 1,2,3,6,9 and 18 as it's factors. As 2 and 3 are factors of 18, 6 is also one of the factors. Another example would be the number 24, the factors of 24 are 1,2,3,4,6,8,12 and 24. Again, 2,3 and 6 are factors of 24.

Q2: It is true. 6 has the same factors as 12, as 12 is a multiple of 6.

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True. The product of 2 and 3 is 6.
Just use 6 as an example:
1x6
2x3
All 1,2,3 and 6 are factors of 6.

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False. 12/6 is 2. Therefore in order to guarantee that any number 6 is a factor of 12 is also a factor of, 2 must also be a factor of that number.
Use 18 as an example:
It’s factors are 1,2,3,6,9 and 18
Even though 6 is a factor of 18 12 isn’t

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The lcm of 2,3 is 6. 6 is a factor of 6,when 6 is multipled,the multiplied number will also be a factor of 6 and so also a factor of 2 and 3

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6 can be a multiple of 1,2,3 and 6.1,2,3 and 6 are all factors of 12

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it is true.
2 and 3 are factors of 6.
example:
2x6=12
3x4=12
6x2=12

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it is true.
multiples of 3: 3, 6, 9, 12
multiples of 6: 6, 12

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Q2: True
Factors of 6: 2,3,6
Factors of 12: 2,3,4,6,12

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Because 2 and 3 are factors of 6, and if 6 is a factor of a number then 2 and 3 are also factors of that number

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6 can be a multiple of 1,2,3 and 6 and 1,2,3 and 6 are all factors of 12