A number is divisible by $18$ , if it is divisible by both $3$ and $6$ .

True

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False

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Solution

The correct option is B False
Given that a number is divisible by both $3$ and $6$ .
We have to find whether the number is divisible by $18$ or not.
We know that If a number is divisible by any other number then it will also be divisible by each of the factors of that number.
Factors of $18 = 1, 2, 3, 6, 9, 18$
Thus if a number is divisible by $18$ then it will also be divisible by each of the factors $1, 2, 3, 6, 9$ not only $3$ and $6$ .
For example: $12$ is divisible by both $3$ and $6$ but is not divisible by $18$ .
Therefore the given statement is false.

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Similar questions

Q. Write (T) for true and (F) for false against each of the following statements:
(i) If a number is divisible by 4, it must be divisible by 8.
(ii) If a number is divisible by 8, it must be divisible by 4.
(iii) If a number divides the sum of two numbers exactly, it must exactly divide the numbers separately.
(iv) If a number is divisible by both 9 and 10, it must be divisible by 90.
(v) A number is divisible by 18 if it is divisible by both 3 and 6.
(vi) If a number is divisible by 3 and 7, it must be divisible by 21.
(vii) The sum of two consecutive odd numbers is always divisible by 4.
(viii) If a number divides two numbers exactly, it must divide their sum exactly.

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.
(iv) If a number is divisible by 8, it must be divisible by 4.
(v) A number is divisible by 18, if it is divisible by both 3 and 6.
(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.
(viii) If a number divides three numbers exactly, it must divide their sum exactly.
(ix) If two numbers are co-prime, at least one of them must be a prime number
(x) The sum of two consecutive odd numbers is always divisible by 4.

Q. A number is divisible by 18, if it is divisible by both 3 and 6

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.

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