$18$ is divisible by both $2$ and $3 .$ . It is also divisible by $2 x 3 = 6 .$ Similarly, a number is divisble by $4$ and $6$ . Can we say that the number must be divisible by $4 x 6 = 24 ?$ If not, give an example to justify your answer.

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Solution

Let us consider the numbers which are divisible by $4$
$4, 8, 12, 16, 20, 24, 28, 32, 36, 40 \dots .$
Now let us consider the numbers which are divisible by $6$
$6, 12, 18, 24, 30, 36, 42, 48, 54, 60, \dots \dots .$
So the number divisible by both $4$ and $6$ are
$12, 24, \dots \dots .$
But we can observe that number $12, 36, \dots$ are divisible by both $4$ and $6$ but not divisible by $24 .$
Hence $,$ it is concluded that a number divisible by $4$ and $6$ is not divisible by $24 .$

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(ii) which is divisible by 4 but not by 8.
(iii) which is divisible by both 2 and 8 but not by 16.
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Q. Which of the following statements are true?

(i) If a number is divisible by 3, it must be divisible by 9.
(ii) If a number is divisible by 9, it must be divisible by 3.
(iii) If a number is divisible by 4, it must be divisible by 8.
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(vi) If a number is divisible by both 9 and 10, it must be divisible by 90.
(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
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(x) The sum of two consecutive odd numbers is always divisible by 4.

18

is divisible by both

2

and

3

.It is also divisible by

2 \times 3 = 6.

4

and

6.

Can we say that the number must also be divisible by

4 \times 6 = 24

?If not, give an example to justify your answer.

Question 11

18 is divisible by both 2 and 3. It is also divisible by $2 \times 3 = 6.$ Similarly, a number is divisible by 4 and 6. Can we say that the number must be divisible by $4 \times 6 = 24 ?$ If not, give an example to justify your answer.

True or False.

4) If a number is divisible by both 9 and 10. It must be divisible by 90.

5) A number is divisible by 18 if it is divisible by both 3 and 6.

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18 is divisible by both 2 and 3.. It is also divisible by 2x3=6. Similarly, a number is divisble by 4 and 6. Can we say that the number must be divisible by 4x6=24? If not, give an example to justify your answer.

$18$ is divisible by both $2$ and $3 .$ . It is also divisible by $2 x 3 = 6 .$ Similarly, a number is divisble by $4$ and $6$ . Can we say that the number must be divisible by $4 x 6 = 24 ?$ If not, give an example to justify your answer.