126 LearnersLast updated on May 26th, 2025
Divisibility Rule of 14
The divisibility rule is a way to find out 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 things. In this topic, we will learn about the divisibility rule of 14.
What is the Divisibility Rule of 14?
The divisibility rule for 14 is a method by which we can find out if a number is divisible by 14 or not without using the division method. A number is divisible by 14 if it is divisible by both 2 and 7. Check whether 308 is divisible by 14 with the divisibility rule.
Step 1: Check divisibility by 2. A number is divisible by 2 if its last digit is even. Here, the last digit of 308 is 8, which is even.
Step 2: Check divisibility by 7 using its rule. Multiply the last digit of the number by 2, and subtract the result from the remaining values without the last digit. In 308, the last digit is 8. Multiply it by 2: 8 × 2 = 16. Subtract 16 from the remaining number: 30 - 16 = 14.
Step 3: Since 14 is a multiple of 7, the number is divisible by 7. Therefore, 308 is divisible by both 2 and 7, and thus by 14.
Tips and Tricks for Divisibility Rule of 14
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 14.
Know the multiples of 14:
Memorize the multiples of 14 (14, 28, 42, 56, etc.) to quickly check divisibility. If a number is a multiple of 14, then it is divisible by 14.
Use divisibility rules for 2 and 7:
Ensure a number is divisible by both 2 and 7 to confirm divisibility by 14.
Repeat the process for large numbers:
Students should keep repeating the divisibility process until they reach a small number that is divisible by both 2 and 7. For example, check if 1946 is divisible by 14. First, check divisibility by 2 (it ends in 6, so yes). Then, for divisibility by 7, multiply the last digit by 2: 6 × 2 = 12. Subtract 12 from 194: 194 - 12 = 182. Repeat for 182: 2 × 2 = 4, 18 - 4 = 14. As 14 is a multiple of 7, 1946 is divisible by 14.
Use the division method to verify: Students can use the division method as a way to verify and crosscheck their results. This helps them verify and learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 14
The divisibility rule of 14 helps us quickly check if the given number is divisible by 14, but common mistakes like calculation errors lead to incorrect results. Here, we will understand some common mistakes that will help you avoid them.
Mistake 1
Not checking both divisibility rules.
To apply the rule of 14, check divisibility by both 2 and 7.
Mistake 2
Including the last digit incorrectly in subtraction.
Exclude the last digit from the remaining number during subtraction when checking divisibility by 7.
Mistake 3
Not repeating the process when the result is large.
Continue the process until you get a small number that can be easily checked for divisibility.
Mistake 4
Confusing divisibility rules for 2 and 7.
Practice and remember that divisibility by 2 requires an even last digit, and for 7, use the specific subtraction method.
Mistake 5
Overlooking one of the divisibility checks.
Ensure that both divisibility checks (for 2 and 7) are satisfied to confirm divisibility by 14.
Divisibility Rule of 14 Examples
Problem 1
A clock tower chimes every 196 minutes. Is the number of minutes (196) divisible by 14?
Yes, 196 is divisible by 14.
Explanation
To determine if 196 is divisible by 14, we need to check divisibility by both 2 and 7.
1) Check divisibility by 2: The last digit of 196 is 6, which is even, so 196 is divisible by 2.
2) Check divisibility by 7:
Multiply the last digit by 2: 6 × 2 = 12.
Subtract from the rest of the number: 19 – 12 = 7.
7 is a multiple of 7.
Since 196 is divisible by both 2 and 7, it is divisible by 14.
Problem 2
A farmer has 462 apples and wants to pack them into cartons, each containing 14 apples. Can he do this without any apples left over?
Yes, 462 is divisible by 14.
Explanation
To check if 462 is divisible by 14, verify divisibility by both 2 and 7.
1) Check divisibility by 2: The last digit is 2, which is even, so 462 is divisible by 2.
2) Check divisibility by 7:
Multiply the last digit by 2: 2 × 2 = 4.
Subtract from the rest of the number: 46 - 4 = 42.
42 is a multiple of 7 (7 × 6 = 42).
Since 462 is divisible by both 2 and 7, it is divisible by 14.
Problem 3
A festival committee plans to distribute 616 free tickets evenly across 14 community centers. Is the number 616 divisible by 14?
Yes, 616 is divisible by 14.
Explanation
To check divisibility by 14, confirm divisibility by 2 and 7.
1) Check divisibility by 2: The last digit is 6, which is even, so 616 is divisible by 2.
2) Check divisibility by 7:
Multiply the last digit by 2: 6 × 2 = 12.
Subtract from the rest of the number: 61 - 12 = 49.
49 is a multiple of 7 (7 × 7 = 49).
Since 616 is divisible by both 2 and 7, it is divisible by 14.
Problem 4
A company has a shipment of 345 products and needs to pack them in boxes of 14. Is 345 divisible by 14?
No, 345 is not divisible by 14.
Explanation
To check if 345 is divisible by 14, verify divisibility by both 2 and 7.
1) Check divisibility by 2: The last digit is 5, which is not even, so 345 is not divisible by 2.
2) Since it's not divisible by 2, it cannot be divisible by 14.
Problem 5
A sports event schedules 784 participants into relay teams, each with 14 members. Can they be divided evenly?
Yes, 784 is divisible by 14.
Explanation
To determine if 784 is divisible by 14, check divisibility by 2 and 7.
1) Check divisibility by 2: The last digit is 4, which is even, so 784 is divisible by 2.
2) Check divisibility by 7:
Multiply the last digit by 2: 4 × 2 = 8.
Subtract from the rest of the number: 78 - 8 = 70.
70 is a multiple of 7 (7 × 10 = 70).
Since 784 is divisible by both 2 and 7, it is divisible by 14.
FAQs on Divisibility Rule of 14
1.What is the divisibility rule for 14?
2.How many numbers are there between 1 and 100 that are divisible by 14?
3.Is 56 divisible by 14?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 14 apply to all integers?
6.How can children in United Kingdom use numbers in everyday life to understand Divisibility Rule of 14?
7.What are some fun ways kids in United Kingdom can practice Divisibility Rule of 14 with numbers?
8.What role do numbers and Divisibility Rule of 14 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Divisibility Rule of 14 skills?
Important Glossaries for Divisibility Rule of 14
- Divisibility rule: The set of rules used to determine if a number is divisible by another number without performing actual division.
- Multiples: The results obtained by multiplying a number by an integer. For example, multiples of 14 are 14, 28, 42, etc.
- Integers: Whole numbers that can be positive, negative, or zero.
- Even Number: A number that is divisible by 2 without a remainder.
- Subtraction: The process of finding the difference between two numbers by reducing one number from another.
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About BrightChamps in United Kingdom
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.
