**Divisibility by 3 questions :**

Here we are going to see some practice questions on divisibility by 3.

Before that let use what is the rule for any number divisible by 3.

Whenever we need to check whether the given number is divisible by 3 or not, first we have to calculate the sum of the digits.If the sum of the digits is divisible by 3, we can say it is divisible by 3.In other wards we can say a number is divisible by 3 if the sum of the digits is divisible by 3.

(1) Which of the following number should be added with 57323 to make this number divisible by 3?

Options :

(A) 2

(B) 1

(C) 0

(2) Which of the following number should be added with 7261 to make this number divisible by 3?

Options :

(A) 0

(B) 3

(C) 2

(3) Are all numbers which are divisible by 9 divisible by 3?

Options :

(A) Yes

(B) No

(4) 54_562 this number is divisible by 3. Fill in the blank with any following suitable digit.

Options :

(A) 6

(B) 8

(C) 1

(5) How many one digit numbers are divisible by 3.

Options :

(A) Two

(B) Six

(C) Three

**Question 1 :**

Which of the following number should be added with 57323 to make this number divisible by 3?

Options :

(A) 2

(B) 1

(C) 0

**Solution :**

First let us find the sum of the digits of the given number, 5 + 7 + 3 + 2 + 3 = 20

20 + 2 = 22 (not divisible by 3)

**20 + 1 = 21 (divisible by 3)**

20 + 0 = 20 (not divisible by 3)

Hence, 1 should be added with 57323 to make this number divisible by 3.

**Question 2 : **

Which of the following number should be added with 7261 to make this number divisible by 3?

Options :

(A) 0

(B) 3

(C) 2

**Solution :**

First let us find the sum of the digits of the given number, 7 + 2 + 6 + 1 = 16

16 + 0 = 16 (not divisible by 3)

16 + 3 = 19 (not divisible by 3)

**16 + 2 = 18 (divisible by 3)**

Hence, 2 should be added with 7261 to make this number divisible by 3.

**Question 3 :**

Are all numbers which are divisible by 9 divisible by 3?

Options :

(A) Yes

(B) No

**Solution :**

Working rule for divisibility by 3 and 9 are same, the multiples of 9 is divisible by 3.

Hence all number which are divisible by 9 is divisible by 3.

**Question 4 :**

54_562 this number is divisible by 3. Fill in the blank with any following suitable digit.

Options :

(A) 6

(B) 8

(C) 1

**Solution :**

Let x be the unknown number.

**Option A :**

5 + 4 + x + 5 + 6 + 2 = 22 + x

If x = 6, then 22 + x = 22 + 6 = 28 (not divisible by 3)

**Option B :**

**If x = 8, then 22 + x = 22 + 8 = 30 (divisible by 3)**

**Option C :**

If x = 1, then 22 + x = 22 + 1 = 23 (not divisible by 3)

Hence 8 is the suitable digit.

**Question 5 :**

How many one digit numbers are divisible by 3.

Options :

(A) Two

(B) Six

(C) Three

**Solution :**

Writing the multiples of 3, we get

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, ...............

Hence three one digit numbers are divisible by 3.

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