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146 LearnersLast updated on February 17th, 2025
Divisibility Rule of 126
The divisibility rule is a way to determine if a number is divisible by another number without using the division method. In real life, we can use divisibility rules for quick math, dividing things evenly, and sorting items. In this topic, we will learn about the divisibility rule of 126.
What is the Divisibility Rule of 126?
The divisibility rule for 126 is a method by which we can find out if a number is divisible by 126 or not without using the division method. To determine if a number is divisible by 126, it must be divisible by 2, 3, and 7, since 126 = 2 × 3 × 7.
Example: Check whether 504 is divisible by 126 using the divisibility rule.
Step 1: Check divisibility by 2. A number is divisible by 2 if its last digit is even. Here, 504 ends in 4, which is even, so it is divisible by 2.
Step 2: Check divisibility by 3. A number is divisible by 3 if the sum of its digits is divisible by 3. For 504, the sum is 5 + 0 + 4 = 9. Since 9 is divisible by 3, 504 is divisible by 3.
Step 3: Check divisibility by 7. Use the divisibility rule of 7: double the last digit and subtract it from the rest of the number. For 504, double 4 to get 8, then subtract 8 from 50, resulting in 42. Since 42 is divisible by 7, 504 is divisible by 7.
Since 504 is divisible by 2, 3, and 7, it is also divisible by 126.
Tips and Tricks for Divisibility Rule of 126
Learning the divisibility rule can help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 126.
- Break it down: Memorize the rules for divisibility by 2, 3, and 7 to simplify checking for divisibility by 126.
- Quick checks: Start by checking divisibility by 2 (even number), then 3 (sum of digits), and finally 7 (subtract twice the last digit from the rest).
- Repeat the process for large numbers: Keep repeating the divisibility process if necessary until you confirm divisibility by 2, 3, and 7.
- Use the division method to verify: Use division to verify and crosscheck results, reinforcing understanding.
Common Mistakes and How to Avoid Them in Divisibility Rule of 126
Divisibility Rule of 126 Examples
Problem 1
A theater sells tickets in blocks of 126. If a group purchases 504 tickets, is this number divisible by 126?
Explanation
Problem 2
A company plans to distribute 1134 promotional items evenly among 9 teams. Is 1134 divisible by 126?
Explanation
Problem 3
An art exhibition plans to display 630 paintings in sections, with each section containing 126 paintings. Is 630 divisible by 126?
Explanation
Problem 4
A library categorizes its books into sets of 126. If there are 882 books, can they be evenly divided into these sets?
Explanation
Problem 5
A concert organizer has 756 tickets to distribute in batches of 126. Are 756 tickets divisible by 126?
Explanation
FAQs on Divisibility Rule of 126
1. What is the divisibility rule for 126?
2.How many numbers between 1 and 1000 are divisible by 126?
3.Is 378 divisible by 126?
4.What if I get a remainder of 0 after division?
5.Does the divisibility rule of 126 apply to all integers?
Important Glossaries for Divisibility Rule of 126
- Divisibility Rule: A set of rules used to determine if a number is divisible by another number without division.
- Multiples: Results obtained after multiplying a number by an integer. Example: multiples of 126 are 126, 252, 378, etc.
- Integers: Whole numbers, including negative numbers and zero.
- Even Numbers: Numbers divisible by 2, such as 2, 4, 6, etc.
- Sum of Digits: The total obtained by adding all the digits in a number, used in divisibility checks like for 3.
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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.
