204 LearnersLast updated on May 26th, 2025
Divisibility Rule of 420
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 420.
What is the Divisibility Rule of 420?
The divisibility rule for 420 is a method by which we can find out if a number is divisible by 420 or not without using the division method. Check whether 840 is divisible by 420 with the divisibility rule.
Step 1: Check if the number is divisible by 10. Since 840 ends in 0, it is divisible by 10.
Step 2: Check if the number is divisible by 42. Divide 840 by 10 to get 84. Check if 84 is divisible by 42.
Step 3: Since 84 divided by 42 equals 2, it is divisible by 42. Therefore, 840 is divisible by 420.
Tips and Tricks for Divisibility Rule of 420
Learning divisibility rules helps to master division. Let’s learn a few tips and tricks for the divisibility rule of 420.
Know the multiples of 420:
Memorize the multiples of 420 (420, 840, 1260, 1680, etc.) to quickly check divisibility. If the result from the division is a whole number, then the original number is divisible by 420.
Break down the rule:
Remember that a number is divisible by 420 if it is divisible by both 10 and 42. Check these smaller divisibility rules separately.
Repeat the process for large numbers:
For large numbers, break them down step-by-step to check divisibility. For example, check if 1680 is divisible by 420. First, confirm it ends in 0, then check if 168 is divisible by 42. Since 168 divided by 42 equals 4, 1680 is divisible by 420.
Use the division method to verify:
Use the division method as a way to verify and crosscheck the results. This will help confirm accuracy and understanding.
Common Mistakes and How to Avoid Them in Divisibility Rule of 420
The divisibility rule of 420 helps us to quickly check if a given number is divisible by 420, 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.
Follow the correct steps: ensure divisibility by 10 and then by 42.
Divisibility Rule of 420 Examples
Problem 1
Is the number of guests, 840, divisible by 420?
Yes, 840 is divisible by 420.
Explanation
To verify if 840 is divisible by 420, we check the divisibility by 4, 3, and 5 (since 420 = 4 x 3 x 5 x 7, and 7 is already checked when confirming 3 and 5).
1) Check divisibility by 4: The last two digits of 840 are 40, which is divisible by 4.
2) Check divisibility by 3: The sum of the digits is 8 + 4 + 0 = 12, which is divisible by 3.
3) Check divisibility by 5: The last digit is 0, which is divisible by 5.
4) Since 840 is divisible by 4, 3, and 5, it is divisible by 420.
Problem 2
A shipment of 1260 items needs to be divided equally into boxes of 420. Is this possible?
Yes, 1260 is divisible by 420.
Explanation
To determine if 1260 can be divided equally into boxes of 420, we check divisibility by 4, 3, and 5.
1) Check divisibility by 4: The last two digits of 1260 are 60, which is divisible by 4.
2) Check divisibility by 3: The sum of the digits is 1 + 2 + 6 + 0 = 9, which is divisible by 3.
3) Check divisibility by 5: The last digit is 0, which is divisible by 5.
4) Since 1260 is divisible by 4, 3, and 5, it is divisible by 420.
Problem 3
A factory produces 210 products per day and wants to package them in boxes of 420. Can they do this at the end of two days?
Yes, 420 is divisible by 420.
Explanation
To check if 420 products can be packaged in boxes of 420, verify divisibility by 4, 3, and 5.
1) Check divisibility by 4: The last two digits 20 are not divisible by 4. However, because 420 is an exact number, the divisibility is inherently true (420/420 = 1).
2) Check divisibility by 3: The sum of the digits is 4 + 2 + 0 = 6, which is divisible by 3.
3) Check divisibility by 5: The last digit is 0, which is divisible by 5.
4) Since the conditions for divisibility by 420 are met (and it's the whole number itself), the packaging is possible.
Problem 4
An event planner has 126 chairs and wants to organize them into groups of 420 for a large event. Is this feasible?
No, 126 is not divisible by 420.
Explanation
To determine if 126 can be grouped into 420, check divisibility by 4, 3, and 5.
1) Check divisibility by 4: The last two digits are 26, which is not divisible by 4.
2) Check divisibility by 3: The sum of the digits is 1 + 2 + 6 = 9, which is divisible by 3.
3) Check divisibility by 5: The last digit is 6, which is not divisible by 5.
4) Since 126 is not divisible by 4 and 5, it is not divisible by 420.
Problem 5
A bakery produces 2100 cupcakes. Can they be packed into boxes of 420 cupcakes each?
Yes, 2100 is divisible by 420.
Explanation
To verify if 2100 can be packed into boxes of 420, we check divisibility by 4, 3, and 5.
1) Check divisibility by 4: The last two digits of 2100 are 00, which is divisible by 4.
2) Check divisibility by 3: The sum of the digits is 2 + 1 + 0 + 0 = 3, which is divisible by 3.
3) Check divisibility by 5: The last digit is 0, which is divisible by 5.
4) Since 2100 is divisible by 4, 3, and 5, it is divisible by 420.
FAQs on Divisibility Rule of 420
1.What is the divisibility rule for 420?
2.How many numbers are there between 1 and 2000 that are divisible by 420?
3.Is 1260 divisible by 420?
4.What if a number ends in a digit other than 0?
5.Does the divisibility rule of 420 apply to all integers?
6.How can children in India use numbers in everyday life to understand Divisibility Rule of 420?
7.What are some fun ways kids in India can practice Divisibility Rule of 420 with numbers?
8.What role do numbers and Divisibility Rule of 420 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 420 skills?
Important Glossaries for Divisibility Rule of 420
- 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. For example, multiples of 420 are 420, 840, 1260, etc.
- Integers: Integers are numbers that include all whole numbers, negative numbers, and zero.
- Subtraction: Subtraction is a process of finding the difference between two numbers by reducing one number from another.
- Division: Division is a mathematical operation where a number is evenly distributed into equal parts or groups.
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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
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