Practice Questions on Divisibility Rules
Last Updated :
15 Jul, 2024
Divisibility rules are the rules that help us calculate difficult problems more simply they help to determine if a number is divisible by another number. And solving Practice Questions on Divisibility Rules are the best way to understand and master the concept of divisibility rules.
In this article, we will learn about the Divisibility rules and solve some Practice Questions on Divisibility Rules to better understand their application and uses.
What are Divisibility Rules?
A divisibility rule is a set of rules that enables us to know whether a particular number is divisible by a divisor by simply looking at its digits instead of going through the complete division operation.
Divisibility RulesBy using divisibility rules, we can determine whether an integer is divisible by another integer or not.
Important Formulas
Various formulas for Divisibility Rules are:
Divisibility Rules | Formula | Example |
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Divisibility for 2 | For divisible by 2, the number's unit digit is 0,2,4,6 or 8. | For example, 100, 222, 344, and 1658 are divisible by 2. |
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Divisibility for 3 | A number is divisible by 3 if the sum of its digits is completely divisible by 3. | For example, 27648 is divisible by 3 check it. Sum of digits = 2 + 7 + 6 + 4 + 8 = 27; 27 ÷ 3 = 9. Hence 27648 is divisible by 3. |
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Divisibility by 4 | A number is divisible by 4 if the last two digits of that number are divisible by 4. | For example, Check if 1124 is divisible by 4. The last 2 digits are 24 which is divisible by 4. So 1124 is divisible by 4. |
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Divisibility for 5 | The number must contains it's unit digit is 0 or 5. | For example, 10000, 2255, 65, 80, 925 are divisible by 5. |
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Divisibility for 6 | The number is divisible by both 2 and 3, then it is divisible by 6. | For example 12, 18, etc. |
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Divisibility for 8 | For the divisibility of 8 the number's last three digits is totally divisible by 8. | For example, 24, 80, 96, etc are divisible by 8. |
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Divisibility for 9 | A number is divisible by 9 if sum of all its digits is completely divisible by 9. | For example, Check if 16911 is divisible by 9 or not? Sum of digits = 1 + 6 + 9 + 1 + 1 = 18. It is exactly divisible by 9. |
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Divisibility for 10 | Divisibility of 10 is that if its unit digit is 0. | For example, 8000, 9010, 11020, 98670 are divisible by 10. |
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Divisibility by 11 | A number is divisible by 11 if difference between sum of digits at odd places and sum of digits at even places is either 0 or is divisible by 11. | For example, 121, 1331, 77, etc are divisible by 10. |
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Practice Questions on Divisibility Rules with Solution
These Practice Questions on Divisibility Rules will help you understand their application and usage in various mathematical problems.
Problem 1: Use divisibility rules to check whether 448 is divisible by 4 or not?
We know that,
Divisibility rule of 4 is when the last two digits are completely divisible by 4 then the number is divisible by 4.
The last two digits we have is 48 and we know that 48 is divisible by 4 in 12 times.
So, Yes 448 is completely divisible by 4.
Problem 2: Use divisibility rules to check whether 1024 is divisible by 2 or not?
We know that,
Divisibilty rule of 2 is if its unit digit is 0,2,4,6 or 8.
In 1024 the last digit is 4 so it is divisible by 2.
Yes, 1024 is divisible by 2.
Problem 3: Use divisibility rules to check whether 1331 is divisible by 11 or not?
We know that,
Divisibilty of 11 is if difference between sum of digits at odd places and sum of digits at even places is either 0 or is divisible by 11.
In 1331, the sum of digits at odd place is 1 + 3 = 4 and the sum of digits at even place is 1 + 3= 4.
So, difference between digits at odd place and digits at even place is 4 - 4 = 0.
Yes 1331 is divisible by 11.
Problem 4: Use divisibility rules to check whether 1238913 is divisible by 3 or not?
We know that,
Disibility of 3 is the sum of all digits must be a multiple of 3.
In 1238913 the sum of every digit is 1 + 2 +3+ 8+ 9+ 1+ 3 = 27 and 27 is multiple of 3.
So Yes, 1238913 is divisible by 3.
Problem 5: Determine if 524 is divisible by 2.
We know that,
A number is divisible by 2 if its last digit is even.
Last Digit of 524: 4 (which is even)
524 is divisible by 2.
Practice Questions on Divisibility Rules : Worksheet
Solve these worksheet containing Practice Questions on Divisibility Rules to test your understanding on the concept of Divisibility Rules.
Q1: Use divisibility rules to check whether 14356 is divisible by 3 or not?
Q2: Use divisibility rules to check whether 3476580 is divisible by 2 or not?
Q3: Use divisibility rules to check whether 34543110 is divisible by 5 or not?
Q4: Use divisibility rules to check whether 572 is divisible by 4 or not?
Q5: Use divisibility rules to check whether 222582 is divisible by 3 or not?
Q6: Use divisibility rules to check whether 1088 is divisible by 8 or not?
Q7: Use divisibility rules to check whether 8565 is divisible by 3 or not?
Q8: Use divisibility rules to check whether 9721 is divisible by 3 or not?