224 LearnersLast updated on May 26th, 2025
Divisibility Rule of 421
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 421.
What is the Divisibility Rule of 421?
The divisibility rule for 421 is a method by which we can find out if a number is divisible by 421 or not without using the division method. Check whether 842 is divisible by 421 with the divisibility rule.
Step 1: Divide the number into groups of three digits starting from the right. If the last group is smaller than three digits, consider it as it is. Here, 842 is already one group.
Step 2: Check if the number in each group is divisible by 421. In our case, check if 842 is divisible by 421.
Step 3: If all groups are divisible by 421, then the entire number is divisible by 421. If not, then the number isn't divisible by 421.
Tips and Tricks for Divisibility Rule of 421
Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 421.
Know the multiples of 421:
Memorize the multiples of 421 (421, 842, 1263, 1684…etc.) to quickly check divisibility. If the number in the group is a multiple of 421, then the number is divisible by 421.
Use smaller numbers:
If the number is smaller than 421, directly check if it is 421 or 0.
Repeat the process for large numbers:
Students should keep dividing the number into groups and checking each group until they confirm divisibility by 421.
Example: Check if 1684 is divisible by 421 using the divisibility test. Divide 1684 into groups: 1 and 684. Check each group. 684 is 421 × 1 + 263 (not divisible), so the number is not divisible by 421.
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 to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 421
The divisibility rule of 421 helps us to quickly check if the given number is divisible by 421, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes that will help you to understand.
Mistake 1
Not dividing the number correctly into groups.
Students should correctly divide the number into groups of three starting from the right.
Mistake 2
Assuming all groups need to be the same size.
The last group can be less than three digits.
Mistake 3
Not checking each group individually.
Ensure each group is checked for divisibility by 421.
Mistake 4
Ignoring remainders in calculations.
Remember to consider remainders when checking for divisibility.
Mistake 5
Confusing the steps.
Students often confuse the steps or forget the steps; to avoid the error, students should practice regularly.
Divisibility Rule of 421 Examples
Problem 1
Is 842 divisible by 421?
Yes, 842 is divisible by 421.
Explanation
To check divisibility by 421, we can use the rule:
1) Divide the number by 421.
2) 842 ÷ 421 = 2.
3) Since the result is an integer, 842 is divisible by 421.
Problem 2
Check the divisibility rule of 421 for 1263.
No, 1263 is not divisible by 421.
Explanation
For checking divisibility by 421,
1) Divide the number by 421.
2) 1263 ÷ 421 = 3.
3) Since the result is an integer, 1263 is divisible by 421. (Please note that this was incorrect. I apologize for the mistake, let's correct it.)
Correction: The correct process should have found that 1263 ÷ 421 = 3 exactly, thus making it divisible.
Problem 3
Is -842 divisible by 421?
Yes, -842 is divisible by 421.
Explanation
To determine if -842 is divisible by 421, first ignore the negative sign.
1) Divide the absolute value by 421.
2) 842 ÷ 421 = 2.
3) Since the result is an integer, -842 is divisible by 421.
Problem 4
Can 1300 be divisible by 421 following the divisibility rule?
No, 1300 isn't divisible by 421.
Explanation
To check if 1300 is divisible by 421:
1) Divide the number by 421.
2) 1300 ÷ 421 ≈ 3.087.
3) Since the result is not an integer, 1300 is not divisible by 421.
Problem 5
Check the divisibility rule of 421 for 2105.
Yes, 2105 is divisible by 421.
Explanation
To check divisibility by 421:
1) Divide the number by 421.
2) 2105 ÷ 421 = 5.
3) Since the result is an integer, 2105 is divisible by 421.
FAQs on Divisibility Rule of 421
1.What is the divisibility rule for 421?
2.How many numbers are there between 1 and 1000 that are divisible by 421?
3.Is 1263 divisible by 421?
4.What if I get 0 in one of the groups?
5.Does the divisibility rule of 421 apply to all integers?
6.How can children in India use numbers in everyday life to understand Divisibility Rule of 421?
7.What are some fun ways kids in India can practice Divisibility Rule of 421 with numbers?
8.What role do numbers and Divisibility Rule of 421 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Divisibility Rule of 421 skills?
Important Glossaries for Divisibility Rule of 421
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Multiples: Multiples are the results we get after multiplying a number by an integer.
- Integer: Integers are numbers that include all the whole numbers, negative numbers, and zero.
- Remainder: The amount left over after division when one number does not divide another exactly.
- Grouping: The process of dividing a number into parts for easier calculation and analysis.
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About BrightChamps in India
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.
