178 LearnersLast updated on May 26th, 2025
Divisibility Rule of 214
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 214.
What is the Divisibility Rule of 214?
The divisibility rule for 214 is a method by which we can find out if a number is divisible by 214 or not without using the division method. Check whether 428 is divisible by 214 using the divisibility rule.
Step 1: Divide the number into groups of three digits from the right. Here in 428, it is already a group of three digits, so no need to divide further.
Step 2: Check if the number itself is 214 or a multiple of 214. If so, then it is divisible by 214. In this case, 428 is not a multiple of 214.
Step 3: If the number is not a multiple, add the digits of the number. For 428, 4 + 2 + 8 = 14.
Step 4: Check if the sum of the digits is a multiple of 214. If not, the number isn’t divisible by 214. Since 14 is not a multiple of 214, 428 is not divisible by 214.
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Tips and Tricks for Divisibility Rule of 214
Learn the divisibility rule to help master division. Let’s learn a few tips and tricks for the divisibility rule of 214.
Know the multiples of 214:
Memorize the multiples of 214 (214, 428, 642, etc.) to quickly check divisibility. If the result from the process is a multiple of 214, the number is divisible by 214.
Use the digit sum:
If the sum of the digits is a multiple of 214, then the number is divisible by 214.
Repeat the process for large numbers:
Students should keep repeating the divisibility process by grouping digits and checking sums until they reach a small sum that is divisible by 214.
Use the division method to verify:
Students can use the division method as a way 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 214
The divisibility rule of 214 helps us quickly check if a given number is divisible by 214, but common mistakes like calculation errors 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: group digits, add the digits, and check if the sum is a multiple of 214.
Mistake 2
Including incorrect groupings.
Ensure digits are grouped correctly and calculations use the correct groupings.
Mistake 3
Not repeating the process when the result is large.
Repeat the process until reaching a small number whose sum is a multiple of 214.
Mistake 4
Ignoring negative results in sums.
Consider the absolute value of the sum when checking for multiples of 214.
Mistake 5
Confusing the steps.
Practice regularly to remember the steps and avoid errors.
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Divisibility Rule of 214 Examples
Problem 1
Is 428 divisible by 214?
Yes, 428 is divisible by 214
Explanation
To check divisibility by 214, divide the number directly by 214.
1) Divide 428 by 214, which gives 2.
2) Since the result is a whole number, 428 is divisible by 214.
Problem 2
Determine if 642 is divisible by 214.
No, 642 is not divisible by 214.
Explanation
To determine divisibility by 214, divide the number directly by 214.
1) Divide 642 by 214, which gives approximately 3.
2) Since the result is not a whole number, 642 is not divisible by 214.
Problem 3
Can -856 be divisible by 214?
Yes, -856 is divisible by 214.
Explanation
To check divisibility, ignore the negative sign and divide the number by 214.
1) Divide 856 by 214, which gives 4.
2) Since the result is a whole number, -856 is divisible by 214.
Problem 4
Is 321 divisible by 214?
No, 321 is not divisible by 214.
Explanation
To check the divisibility by 214, divide 321 by 214.
1) Divide 321 by 214, which gives approximately 1.5.
2) Since the result is not a whole number, 321 is not divisible by 214.
Problem 5
Check if 1926 is divisible by 214.
Yes, 1926 is divisible by 214.
Explanation
To verify divisibility by 214, divide the number directly by 214.
1) Divide 1926 by 214, which gives 9.
2) Since the result is a whole number, 1926 is divisible by 214.
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FAQs on Divisibility Rule of 214
1.What is the divisibility rule for 214?
2.How many numbers are there between 1 and 1000 that are divisible by 214?
3. Is 642 divisible by 214?
4. What if I get 0 after adding the digits?
5. Does the divisibility rule of 214 apply to all integers?
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Important Glossaries for Divisibility Rule of 214
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Multiples: The results we get after multiplying a number by an integer. For example, multiples of 214 are 214, 428, 642, etc.
- Digit sum: The process of adding all the digits of a number.
- Integers: Numbers that include all whole numbers, negative numbers, and zero.
- Verification: The process of checking the correctness of a result, such as using division to confirm divisibility.
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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.
