Divisibility Rule of 3 and 9 – With Examples

Hello students, in this tutorial you will learn and practice the divisibility rule of 3 and divisibility rule of 9 with example questions. These rules are necessary as they help test the divisibilities of large numbers without performing the division.

Also, the rule of divisibility for 3 is necessary as it helps in testing the divisibility by 6 and some other numbers. You will find that in other divisibility rule tutorials.

The rules of divisibility for 3 and 9 are similar and follow the same process. Let’s check the steps to determine the divisibility of a number by 3.

Divisibility rule of 3

It states that if the number formed by adding all the digits of a given number is a multiple of 3 then the given number is divisible by 3.

To test the divisibility by 3, follow the below steps:

1. First, get the sum of all the digits of a number
2. Now, divide the sum with 3
3. If the sum is divisible by 3, then the entire number is divisible by 3

For Examples,

For a number 21591,

The sum of all digits, 2+1+5+9+1 = 18, and 18 is divisible by 3; hence, 21591 is also divisible by 3.

Similarly, 36991 is not divisible by 3 as 3+6+9+9+1 = 28 which is not a multiple of 3.

You may check for the divisibility by 3 of any number (small or large) with this method. Make sure to practice the questions shared below.

Divisibility rule of 9

The divisibility rule of 9 is similar to the divisibility rule of 3. It states, “if the sum of all the digits of a number is divisible by 9, then the number is also divisible by 9”.

Examples,

For a number 2592351, sum of all digits, 2+5+9+2+3+5+1 = 27, which is a multiple of 9. Hence, the entire number 2592351 is also divisible by 9.

On the other hand, 493361 is not divisible by 9 as the sum of digits, 4+9+3+3+6+1 = 26, is not multiple of 9.

You may want to check: Maths formulas for class 9

Practice questions to test the divisibility by 3 and 9

Q1. What is the minimum difference between two numbers divisible by 3?

Q2. Check the divisibility of the following numbers by 3 and 9.

• 456990
• 1300005
• 35661109
• 51469850
• 1919191911
• 93939393939

Q3. Fill in the blanks to make the statement true.

• 4521_ is divisible by 3 but not 9.
• 5412_ is divisible by both 3 and 9.
• 69110_ _ is not divisible by both 3 nor 9.
• 95_33_ is divisible by 9.

Q4. Check whether the following statements are true

• If a number is divisible by 3, it will also be divisible by 9.
• If a number is divisible by 9, it will also be divisible by 3.

Q5. What is the minimum number that should be added to 45699 to make it divisible by 3 but not by 9?

Q6. What is the minimum number that must be added to 311126 so that the new number is divisible by both 3 and 9?

Q7. Sheela packed 9 chocolates in one box. There were a total of 219 chocolates, and she wanted to pack all of them into such boxes. Did any chocolate remain? If yes, how many?

Q8. Can we divide 1,536 students into a group of 9 so that only one student remains?

Q9. Rakesh wanted to give his three friends the same amount of cards. Unfortunately, he lost some of them. If there are 64 cards left, how many cards will he need extra so that each friend receives cards in a multiple of 9?

Q10. Between 1 to 100, how many numbers are divisible by (i) 3 and (ii) 9?

Other important divisibility rules

Divisibility rule of 7	Divisibility rule of 4
Divisibility rule of 25	Divisibility rule of 17

Frequently Asked Questions (FAQs)