Divisibility rules for 2 to 12 with tricks and solved examples
The division is used much more often than you realise. When splitting food or money with friends, or even when slicing a pizza, division is used. Divisibility rules in Maths are a collection of specific criteria that apply to a number to determine whether or not it is divisible by a specified number. Some well-known divisibility rules are for numbers ranging from 2 to 10.
The rules allow us to find factors and multiples of numbers without having to conduct lengthy divisions. By following the divisibility rule formula, a person can determine if a number is divisible by another integer. In this article, we will learn about the divisibility rules with examples.
Division Rule of Integers
In Mathematics, division rules help to identify whether a number is divisible by another number instead of using the actual method of division. If one number is totally divisible by another, the quotient is a whole number, and the remainder is always zero. If a number is not completely divided by any other number, such numbers have a remainder other than zero or nonzero. Now let’s see the divisibility rules with examples one by one.
Division Rule For 2
If you have a number with the last digit as 0 or an even number, it is divisible by 2. For example, the number 20 ends with a zero. When half of a number is split, the outcome is 10, which is an even number.
Example: Check whether the number 257746 is divisible by 2.
Ans: Since the number ends with 6, which is even. Hence the number 257746 is divisible by 2.
Division Rule For 3
If the total of the digits of a number is divisible by three, then the number is divisible by three. Students must be able to divide to apply this strategy, but verifying smaller numbers is easier than large ones. To get more clarity for the divisiblity rule for 3, see the division rules chart given below.
Division Rules Chart for 3
Example: Check whether the number 168 is divisible by 3.
Ans:
$1+6+8=15$
$\Rightarrow \dfrac{15}{3}=5$
As a result, 168 is divisible by 3.
Division Rule for 4
If a number's last two digits are divisible by four, then the whole number is divisible by 4.
Example: Check whether the number 7516 is divisible by 4.
Ans: Since the number 7516 has the last two digits 16, divisible by 4. Hence the number 7516 is divisible by 4.
Division Rule For 5
When the last digit of a number is 0 or 5, the value can be split evenly by 5. As a result, 5, 10, 15, 20, 25, and so on can all be divided by 5.
Example: Check whether the number 160 is divisible by 5.
Ans: Since the last digit of the number 160 is 0. So, 160 is divisible by 5.
Division Rule For 6
Numbers divisible by 6 can also be split by 3 and 2. Students should test the number using both rules for 3 and 2. If the number passes both criteria, it can be divided by 6. If it fails even one test, it cannot pass.
Example: Check whether the number 306 is divisible by 6.
Ans: Since 308 ends in an even digit, it is divisible by two. However, 3 + 0 + 6 Equals 9, which can be divided evenly by 3. As a result, 306 is divisible by 6.
Division Rule For 8
A large number is divisible by 8 if the last three digits are either divisible by 8 or are 000.
Example: Check whether the number 9864 is divisible by 8.
Ans: Since the last three digits are divisible by 8 (i.e. $864 \div 8=108$ ). Hence the number 864 is divisible by 8.
Division Rule For 9
Since 9 can be divided by 3. Therefore, the divisibility rule for 9 is the same as for 3. If the sum of a number's digits is divisible by 9, then the whole number is also divisible.
Example: check whether the following number is divisible by 9 or not.
$549=5+4+9=18$
$\Rightarrow \dfrac{18}{2}=9$
Ans: As a result, 549 is divisible by 9.
Division Rule For 10
If the last digit is 0, the number can be evenly divided by ten.
Example: check whether the no. 1650 is divisible by 10 or not?
Ans: However,1650 ends with 0, which can be divided evenly by 10. As a result, 1650 is divisible by 10.
Solved Example
Example Time
Q 1. Find out if 2415 is divisible by 7 using the divisibility rule of 7.
Ans: Applying the 7-division rule to the number 2415 will reveal whether it is or is not divisible by 7.
Multiply the unit’s digit (5) by 2. The answer is 10.
Take the remainder of the number, 241, and subtract the product (10) from it. (241 - 10 = 231)
We are unsure if 231 is a multiple of 7. Consequently, let's return to step 1 and enter 231 there.
Multiply the unit’s digit (1) by 2. The answer is 2.
Take that number out of the total, which is 23. (23 - 2 = 21)
Since 21 is completely divisible by 7, we can say that 2415 is divisible by 7.
Practice Problems
Q 1. Check whether the number 198 is divisible by 8.
Ans: Not Divisible.
Q 2. Check whether the number 6273 is divisible by 3.
Ans: Yes.
Summary
The divisibility rule enables us to determine whether or not the number is divisible by another number. When two numbers can be divided evenly, the quotient is always a whole number, and the remainder is always zero. If a number is not completely divided by another number, the remainder is not zero or non-zero. It is the easiest and quickest way to solve division.
There are various rules to check divisibility. Some well-known divisibility rules are for numbers between 2 and 10. Hope this article will help you solve the division questions quickly by using the rule we learned.
FAQs on Divisibility Rules in Maths Explained Clearly
1. What are divisibility rules in maths?
Divisibility rules are quick tests used to determine whether one number is exactly divisible by another without performing long division. These rules help check if a number divides evenly (with remainder 0).
- They simplify calculations in arithmetic.
- They are commonly used for numbers like 2, 3, 4, 5, 6, 8, 9, 10, 11.
- They are useful in factoring, simplifying fractions, and finding LCM or HCF.
2. What is the divisibility rule for 2?
A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8). This works because even numbers are multiples of 2.
- Example: 246 → last digit is 6 → divisible by 2.
- Example: 357 → last digit is 7 → not divisible by 2.
3. What is the divisibility rule for 3?
A number is divisible by 3 if the sum of its digits is divisible by 3. Add all digits and check if the result is a multiple of 3.
- Example: 123 → 1 + 2 + 3 = 6 → divisible by 3.
- Example: 124 → 1 + 2 + 4 = 7 → not divisible by 3.
4. What is the divisibility rule for 4?
A number is divisible by 4 if its last two digits form a number divisible by 4. Only the last two digits matter.
- Example: 316 → last two digits are 16 → divisible by 4.
- Example: 318 → last two digits are 18 → not divisible by 4.
5. What is the divisibility rule for 5?
A number is divisible by 5 if its last digit is 0 or 5. This is because all multiples of 5 end in these digits.
- Example: 245 → last digit 5 → divisible by 5.
- Example: 247 → last digit 7 → not divisible by 5.
6. What is the divisibility rule for 6?
A number is divisible by 6 if it is divisible by both 2 and 3. Since 6 = 2 × 3, both conditions must be satisfied.
- Check if the number is even (rule of 2).
- Check if the sum of digits is divisible by 3.
- Example: 126 → even and 1+2+6=9 → divisible by 6.
7. What is the divisibility rule for 8?
A number is divisible by 8 if its last three digits form a number divisible by 8. Only the last three digits need to be checked.
- Example: 1,024 → last three digits are 024 (24) → divisible by 8.
- Example: 1,026 → last three digits are 026 (26) → not divisible by 8.
8. What is the divisibility rule for 9?
A number is divisible by 9 if the sum of its digits is divisible by 9. This is similar to the rule for 3 but checks multiples of 9.
- Example: 729 → 7 + 2 + 9 = 18 → divisible by 9.
- Example: 734 → 7 + 3 + 4 = 14 → not divisible by 9.
9. What is the divisibility rule for 10?
A number is divisible by 10 if its last digit is 0. This is because all multiples of 10 end in zero.
- Example: 450 → last digit 0 → divisible by 10.
- Example: 453 → last digit 3 → not divisible by 10.
10. How do divisibility rules help in finding factors and HCF?
Divisibility rules help identify factors quickly, which makes finding the HCF (Highest Common Factor) and simplifying fractions easier. By checking divisibility, you can break numbers into smaller factors.
- Example: To factor 36, check divisibility by 2, 3, 4, 6, 9.
- 36 is divisible by 2, 3, 4, 6, 9 → so these are its factors.
- This helps in prime factorization and calculating LCM and HCF.
