175 LearnersLast updated on May 26th, 2025
Divisibility Rule of 42
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 42.
What is the Divisibility Rule of 42?
The divisibility rule for 42 is a method by which we can find out if a number is divisible by 42 or not without using the division method. Check whether 252 is divisible by 42 with the divisibility rule.
Step 1: Check if the number is divisible by both 6 and 7.
For divisibility by 6, the last digit must be even, and the sum of the digits must be divisible by 3. For 252, the last digit is 2 (even), and the sum of the digits is 2 + 5 + 2 = 9, which is divisible by 3.
For divisibility by 7, double the last digit and subtract it from the rest of the number. For example, 2 × 2 = 4, and 25 - 4 = 21. Since 21 is divisible by 7, the rule holds.
Step 2: Since 252 meets both criteria, it is divisible by 42.
Tips and Tricks for Divisibility Rule of 42
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 42.
- Know the multiples of 42: Memorize the multiples of 42 (42, 84, 126, 168, 210, etc.) to quickly check the divisibility. If a number is a multiple of both 6 and 7, it is divisible by 42.
- Use the divisibility rules for 6 and 7: Use the divisibility rules for 6 and 7 to determine divisibility by 42. A number must meet both conditions.
- Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by both 6 and 7.
- 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 42
The divisibility rule of 42 helps us to quickly check if the given number is divisible by 42, 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 for 6 and 7.
Ensure you check both divisibility rules for 6 and 7. A number must satisfy both conditions to be divisible by 42.
Divisibility Rule of 42 Examples
Problem 1
Is the number of pages in a book, 420, divisible by 42?
Yes, 420 is divisible by 42.
Explanation
To determine if 420 is divisible by 42, we need to check divisibility by both 6 and 7 (since 42 = 6 x 7).
1) Check divisibility by 6: 420 is even, and the sum of its digits (4 + 2 + 0 = 6) is divisible by 3, so 420 is divisible by 6.
2) Check divisibility by 7:
Multiply the last digit by 2: 0 × 2 = 0.
Subtract from the rest: 42 - 0 = 42.
42 is divisible by 7.
Since 420 is divisible by both 6 and 7, it is divisible by 42.
Problem 2
A club has 294 members. Can they be evenly divided into groups of 42?
Yes, 294 can be evenly divided by 42.
Explanation
To check if 294 is divisible by 42, we need to check divisibility by both 6 and 7.
1) Check divisibility by 6: 294 is even, and the sum of its digits (2 + 9 + 4 = 15) is divisible by 3, so 294 is divisible by 6.
2) Check divisibility by 7:
Multiply the last digit by 2: 4 × 2 = 8.
Subtract from the rest: 29 - 8 = 21.
21 is divisible by 7.
Since 294 is divisible by both 6 and 7, it is divisible by 42.
Problem 3
Is the total number of seats in a theater, 336, divisible by 42?
Yes, 336 is divisible by 42.
Explanation
To determine if 336 is divisible by 42, check for divisibility by both 6 and 7.
1) Check divisibility by 6: 336 is even, and the sum of its digits (3 + 3 + 6 = 12) is divisible by 3, so 336 is divisible by 6.
2) Check divisibility by 7:
Multiply the last digit by 2: 6 × 2 = 12.
Subtract from the rest: 33 - 12 = 21.
21 is divisible by 7.
Since 336 is divisible by both 6 and 7, it is divisible by 42.
Problem 4
A concert venue has 200 seats and wants to arrange them in sections of 42. Is this possible?
No, 200 is not divisible by 42.
Explanation
To check if 200 is divisible by 42, check for divisibility by both 6 and 7.
1) Check divisibility by 6: 200 is even, but the sum of its digits (2 + 0 + 0 = 2) is not divisible by 3, so 200 is not divisible by 6.
Since 200 is not divisible by 6, it cannot be divisible by 42.
Problem 5
A puzzle has 504 pieces. Can these pieces be arranged into sets of 42?
Yes, 504 can be arranged into sets of 42.
Explanation
To determine if 504 is divisible by 42, check for divisibility by both 6 and 7.
1) Check divisibility by 6: 504 is even, and the sum of its digits (5 + 0 + 4 = 9) is divisible by 3, so 504 is divisible by 6.
2) Check divisibility by 7:
Multiply the last digit by 2: 4 × 2 = 8.
Subtract from the rest: 50 - 8 = 42.
42 is divisible by 7.
Since 504 is divisible by both 6 and 7, it is divisible by 42.
FAQs on Divisibility Rule of 42
1.What is the divisibility rule for 42?
2.How many numbers are there between 1 and 100 that are divisible by 42?
3.Is 126 divisible by 42?
4.What if I get 0 after checking divisibility by 7?
5.Does the divisibility rule of 42 apply to all integers?
6.How can children in United Kingdom use numbers in everyday life to understand Divisibility Rule of 42?
7.What are some fun ways kids in United Kingdom can practice Divisibility Rule of 42 with numbers?
8.What role do numbers and Divisibility Rule of 42 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 42 skills?
Important Glossaries for Divisibility Rule of 42.
- Divisibility rule: The set of rules used to determine if a number is divisible by another number without performing division.
- Multiples: Products obtained by multiplying a number by an integer. For example, multiples of 42 are 42, 84, 126, etc.
- Even number: A number that is divisible by 2.
- Sum of digits: The result of adding all the digits of a number together.
- Integer: A whole number that can be positive, negative, or zero.
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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.
