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140 LearnersLast updated on February 17th, 2025
Divisibility Rule of 144
The divisibility rule is a way to determine whether a number is divisible by another number without performing division. In real life, we can use the divisibility rule for quick math, dividing things evenly, and sorting things. In this topic, we will learn about the divisibility rule of 144.
What is the Divisibility Rule of 144?
The divisibility rule for 144 is a method by which we can find out if a number is divisible by 144 without using the division method. Check whether 5184 is divisible by 144 using the divisibility rule.
Step 1: Check if the number is divisible by 12 (since 12 is a factor of 144). A number is divisible by 12 if it is divisible by both 3 and 4.
For divisibility by 3, add the digits of the number: 5 + 1 + 8 + 4 = 18. Since 18 is divisible by 3, 5184 is divisible by 3.
For divisibility by 4, check if the last two digits form a number divisible by 4: 84 is divisible by 4.
Step 2: Check if the number is divisible by 12 again to ensure it's divisible by 144. Since 5184 is divisible by 12, continue testing.
Step 3: Finally, check divisibility by 12 again. Since it passes, 5184 is divisible by 144.
Tips and Tricks for Divisibility Rule of 144
Understanding the divisibility rule will help mastery of division. Let’s learn a few tips and tricks for the divisibility rule of 144.
- Know the multiples of 144: Memorize the multiples of 144 (144, 288, 432, 576, etc.) to quickly check divisibility. If a number is a multiple of 144, it is divisible by 144.
- Break down to factors: Since 144 = 12 × 12, check divisibility by 12 twice to confirm divisibility by 144.
- Use the division method to verify: Students can use the division method to verify and crosscheck their results. This will help them to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 144
The divisibility rule of 144 helps us to quickly check if a given number is divisible by 144, but common mistakes like calculation errors can lead to incorrect results. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not following the correct steps.
Ensure to check divisibility by 12 twice, confirming all steps are followed correctly.
Divisibility Rule of 144 Examples
Problem 1
Is 1728 divisible by 144?
Yes, 1728 is divisible by 144.
Explanation
To check the divisibility of 1728 by 144, we need to ensure it's divisible by both 12 and 12 (since \(144 = 12 \times 12\)).
1) Check divisibility by 12: The sum of the digits (1 + 7 + 2 + 8) = 18, which is divisible by 3. The last two digits, 28, are not divisible by 4 directly, so we check \(28 \div 4 = 7\). Thus, 1728 is divisible by 12.
2) The number 1728 is also divisible by 12 again, confirming that it is divisible by 144.
Problem 2
Check the divisibility rule of 144 for 2592.
Yes, 2592 is divisible by 144.
Explanation
To verify divisibility by 144, we check for divisibility by 12 twice.
1) Check divisibility by 12: The sum of the digits (2 + 5 + 9 + 2) = 18, which is divisible by 3. The last two digits, 92, are divisible by 4 (\(92 \div 4 = 23\)). Therefore, 2592 is divisible by 12.
2) Again, 2592 passes the divisibility check for 12, confirming divisibility by 144.
Problem 3
Is 3456 divisible by 144?
No, 3456 is not divisible by 144.
Explanation
We need to check the divisibility by 12 twice.
1) Check divisibility by 12: The sum of the digits (3 + 4 + 5 + 6) = 18, which is divisible by 3. The last two digits, 56, are divisible by 4 (\(56 \div 4 = 14\)), so 3456 is divisible by 12.
2) Now, check again for divisibility by 12, but the sum of digits (18) and the last two digits (56) do not repeat this pattern consistently, indicating 3456 is not divisible by 144.
Problem 4
Can 1296 be divisible by 144 following the divisibility rule?
Yes, 1296 is divisible by 144.
Explanation
To determine if 1296 is divisible by 144, check divisibility by 12 twice.
1) Check divisibility by 12: The sum of the digits (1 + 2 + 9 + 6) = 18, which is divisible by 3. The last two digits, 96, are divisible by 4 (\(96 \div 4 = 24\)). Therefore, 1296 is divisible by 12.
2) 1296 meets the divisibility requirements of 12 again, confirming that it is divisible by 144.
Problem 5
Check the divisibility rule of 144 for 3888.
No, 3888 is not divisible by 144.
Explanation
To check the divisibility by 144, ensure divisibility by 12 twice.
1) Check divisibility by 12: The sum of the digits (3 + 8 + 8 + 8) = 27, which is divisible by 3. The last two digits, 88, are divisible by 4 (\(88 \div 4 = 22\)). Thus, 3888 is divisible by 12.
2) However, a second check for divisibility by 12 does not hold, as the pattern for 12 does not repeat consistently on the next check, indicating 3888 is not divisible by 144.
FAQs on Divisibility Rule of 144
1.What is the divisibility rule for 144?
2.How many numbers are there between 1 and 1000 that are divisible by 144?
3.Is 576 divisible by 144?
4.What if I get 0 after subtraction during verification?
5.Does the divisibility rule of 144 apply to all integers?
Important Glossaries for Divisibility Rule of 144
- Divisibility rule: A set of rules used to determine whether a number is divisible by another number without actual division.
- Factors: Numbers that are multiplied together to obtain another number. For example, 12 and 12 are factors of 144.
- Multiples: The results obtained by multiplying a number by an integer. For example, multiples of 144 are 144, 288, 432, etc.
- Addition: The process of combining numbers to get a sum, often used in checking divisibility by 3.
- Verification: The process of confirming the result, often by performing the original division to ensure accuracy.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
