135 LearnersLast updated on May 26th, 2025
Divisibility Rule of 114
The divisibility rule is a way to determine whether a number is divisible by another number without using the division method. In real life, we can use the divisibility rule for quick math, dividing things evenly, and sorting items. In this topic, we will learn about the divisibility rule of 114.
What is the Divisibility Rule of 114?
The divisibility rule for 114 is a method by which we can find out if a number is divisible by 114 or not without using the division method. Check whether 684 is divisible by 114 with the divisibility rule.
Step 1: Check if the number is divisible by 2. Since 684 ends in 4, it is divisible by 2.
Step 2: Check if the number is divisible by 3. Add the digits of 684: 6 + 8 + 4 = 18. Since 18 is divisible by 3, so is 684.
Step 3: Check if the number is divisible by 19. Divide 684 by 19 to verify. Since 684 ÷ 19 = 36, which is a whole number, 684 is divisible by 19.
Step 4: Since 684 is divisible by 2, 3, and 19, it is divisible by 114.
Tips and Tricks for Divisibility Rule of 114
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 114.
Know the factors of 114:
Memorize the factors 2, 3, and 19 to quickly check divisibility. If a number is divisible by all three, then the number is divisible by 114.
Use negative numbers:
If you encounter negative numbers, consider their absolute value for checking divisibility.
Repeat the process for large numbers: Repeat divisibility checks for 2, 3, and 19 until the number is reduced to smaller factors.
Use the division method to verify:
Students can use the division method as a way to verify and cross-check their results. This will help them learn and confirm accuracy.
Common Mistakes and How to Avoid Them in Divisibility Rule of 114
The divisibility rule of 114 helps us quickly check if a given number is divisible by 114, but common mistakes can lead to incorrect results. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not following the correct steps.
Students should follow the correct steps by checking divisibility by 2, 3, and 19 separately.
Divisibility Rule of 114 Examples
Problem 1
Is 684 divisible by 114?
Yes, 684 is divisible by 114.
Explanation
To check if 684 is divisible by 114, follow these steps:
1) Break down 684 into the sum of its digits: 6 + 8 + 4 = 18.
2) Check if 18 is divisible by 3 (since 114 is divisible by 3), and it is, as 18 ÷ 3 = 6.
3) Check if the number is divisible by both 2 and 57 (since 114 = 2 × 57).
- 684 is even, so it is divisible by 2.
- 684 ÷ 57 = 12, which means 684 is divisible by 57.
Since 684 is divisible by both 2 and 57, it is divisible by 114.
Problem 2
Check the divisibility rule of 114 for 798.
No, 798 is not divisible by 114.
Explanation
To check if 798 is divisible by 114, follow these steps:
1) Break down 798 into the sum of its digits: 7 + 9 + 8 = 24.
2) Check if 24 is divisible by 3, and it is, as 24 ÷ 3 = 8.
3) Check if the number is divisible by both 2 and 57.
- 798 is even, so it is divisible by 2.
- 798 ÷ 57 = 14, so it is divisible by 57.
Since 798 is divisible by both 2 and 57, it is divisible by 114.
Problem 3
Is -570 divisible by 114?
No, -570 is not divisible by 114.
Explanation
To check if -570 is divisible by 114, follow these steps:
1) Consider the absolute value: 570.
2) Break down 570 into the sum of its digits: 5 + 7 + 0 = 12.
3) Check if 12 is divisible by 3, and it is, as 12 ÷ 3 = 4.
4) Check if the number is divisible by both 2 and 57.
- 570 is even, so it is divisible by 2.
- 570 ÷ 57 = 10, which means 570 is divisible by 57.
Since 570 is divisible by both 2 and 57, it is divisible by 114, but since the original check was negative, the divisibility by 114 holds for the numerical value but not the sign.
Problem 4
Can 912 be divisible by 114 following the divisibility rule?
Yes, 912 is divisible by 114.
Explanation
To check if 912 is divisible by 114, follow these steps:
1) Break down 912 into the sum of its digits: 9 + 1 + 2 = 12.
2) Check if 12 is divisible by 3, and it is, as 12 ÷ 3 = 4.
3) Check if the number is divisible by both 2 and 57.
- 912 is even, so it is divisible by 2.
- 912 ÷ 57 = 16, which means 912 is divisible by 57.
Since 912 is divisible by both 2 and 57, it is divisible by 114.
Problem 5
Check the divisibility rule of 114 for 1026.
Yes, 1026 is divisible by 114.
Explanation
To check if 1026 is divisible by 114, follow these steps:
1) Break down 1026 into the sum of its digits: 1 + 0 + 2 + 6 = 9.
2) Check if 9 is divisible by 3, and it is, as 9 ÷ 3 = 3.
3) Check if the number is divisible by both 2 and 57.
- 1026 is even, so it is divisible by 2.
- 1026 ÷ 57 = 18, which means 1026 is divisible by 57.
Since 1026 is divisible by both 2 and 57, it is divisible by 114.
FAQs on Divisibility Rule of 114
1.What is the divisibility rule for 114?
2.How many numbers are there between 1 and 1,000 that are divisible by 114?
3.Is 684 divisible by 114?
4.What if I get 0 after subtracting or dividing?
5.Does the divisibility rule of 114 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 114?
7.What are some fun ways kids in United States can practice Divisibility Rule of 114 with numbers?
8.What role do numbers and Divisibility Rule of 114 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Divisibility Rule of 114 skills?
Important Glossary for Divisibility Rule of 114
Divisibility rule: A set of rules used to find out whether a number is divisible by another number without performing full division.
Factors: Numbers that divide another number exactly without leaving a remainder. For 114, the factors are 2, 3, and 19.
Absolute value: The non-negative value of a number without regard to its sign.
Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 19 are 19, 38, 57, etc.
Remainder: The amount left over after division when one number doesn't divide another exactly.
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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.
