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

True

No worries! We‘ve got your back. Try BYJU‘S free classes today!

False

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is B False
Step 1: Understanding the tests of divisibility:
Divisibility by $3$ : A number is divisible by $3$ , if sum of its digits is divisible by $3$ .
Divisibility by $6$ : A number is divisible by $6$ , if sum of its digits is divisible by $2$ and $3$ .
Step 2: Check the divisibility tests:
Consider a number $30$
Sum of digits of $30 = 3 + 0 = 3$
Digit at the unit's place of $30 = 0$
Here, $30$ is divisible by $3$ and $6$ , but not divisible by $18$ .
Therefore, the given statement is false.

Suggest Corrections

Similar questions

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

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

State whether the following statement is True or False

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

Join BYJU'S Learning Program

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

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