220 LearnersLast updated on May 26th, 2025
Divisibility Rule of 242
The divisibility rule is a way to determine whether a number is divisible by another number without performing actual division. In real life, we can use the divisibility rule for quick math, dividing things evenly, and sorting items. In this topic, we will learn about the divisibility rule of 242.
What is the Divisibility Rule of 242?
The divisibility rule for 242 is a method by which we can find out if a number is divisible by 242 without using the division method. Let’s check whether 484 is divisible by 242 using the divisibility rule.
Step 1: Check if the number is divisible by 2, 11, and 11. Since 242 is 2 × 11 × 11, a number must be divisible by each of these factors to be divisible by 242.
Step 2: For divisibility by 2, the last digit must be even. In 484, the last digit is 4, which is even.
Step 3: For divisibility by 11, calculate the alternating sum and difference of the digits. For 484, (4 - 8 + 4) = 0, which is a multiple of 11.
Step 4: Repeat Step 3 for the second factor 11, using the same calculation from Step 3, (4 - 8 + 4) = 0, which confirms divisibility by 11 again.
Since 484 meets all conditions, it is divisible by 242.
Tips and Tricks for Divisibility Rule of 242
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 242.
Know the multiples of 242:
Memorize the multiples of 242 (242, 484, 726, etc.) to quickly check divisibility.
Check divisibility by 2, 11, and 11 separately:
A number is divisible by 242 only if it is divisible by 2, 11, and 11.
Repeat the process for large numbers:
For larger numbers, verify divisibility by each factor (2, 11, 11) separately.
Use the division method to verify:
Students can use the division method to verify and cross-check their results. This helps them to verify and learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 242
The divisibility rule of 242 helps us quickly check if a number is divisible by 242, but common mistakes can lead to incorrect conclusions. Here are some common mistakes and how to avoid them:
Mistake 1
Not checking divisibility by all factors (2, 11, 11).
Ensure that the number is divisible by 2, 11, and 11.
Mistake 2
Miscalculating the alternating sum for divisibility by 11.
Carefully calculate the alternating sum and difference of the digits.
Mistake 3
Overlooking the requirement for each factor.
Confirm divisibility by each of the factors (2, 11, 11) separately.
Mistake 4
Confusing the steps for different factors.
Practice regularly to remember the distinct steps for each factor.
Divisibility Rule of 242 Examples
Problem 1
Is 4840 divisible by 242?
Yes, 4840 is divisible by 242.
Explanation
Let's check if 4840 is divisible by 242.
1) Split the number into two parts: 48 and 40.
2) Check if each part is divisible by the corresponding factors of 242, which are 2, 11, and 11.
- 48 is divisible by 2.
- 40 is divisible by 2.
- 48 is not divisible by 11, but 44 is (48 - 4 = 44).
- 40 is not divisible by 11, but 44 is (40 + 4 = 44).
3) Since each part is either divisible or can be adjusted to be divisible by the factors of 242, 4840 is divisible by 242.
Problem 2
Can 7261 be divisible by 242 using the divisibility rule?
No, 7261 is not divisible by 242.
Explanation
To determine if 7261 is divisible by 242:
1) Break the number into two segments: 72 and 61.
2) Check divisibility by the factors of 242 (2, 11, 11).
- 72 is divisible by 2.
- 61 is not divisible by 2.
- 72 is divisible by 11 (72 ÷ 11 = 6.545, not an integer).
- 61 is not divisible by 11.
3) Since both segments do not satisfy divisibility by 11, 7261 is not divisible by 242.
Problem 3
Is -968 divisible by 242?
Yes, -968 is divisible by 242.
Explanation
To check if -968 is divisible by 242, ignore the negative sign:
1) Divide the number into two parts: 96 and 8.
2) Check divisibility by the factors of 242 (2, 11, 11).
- 96 is divisible by 2.
- 8 is divisible by 2.
- 96 is divisible by 11 (96 ÷ 11 = 8.727, not an integer).
- 88 (96 - 8) is divisible by 11.
3) Since the adjusted numbers are divisible by the factors, -968 is divisible by 242.
Problem 4
Check the divisibility rule of 242 for 1452.
No, 1452 is not divisible by 242.
Explanation
To check if 1452 is divisible by 242:
1) Split the number into two parts: 145 and 2.
2) Check divisibility by the factors of 242 (2, 11, 11).
- 145 is divisible by 11 (145 ÷ 11 = 13.18, not an integer).
- 2 is not divisible by 11.
- 145 is not divisible by 2.
3) Since not all parts satisfy the divisibility conditions, 1452 is not divisible by 242.
Problem 5
Is 2420 divisible by 242?
Yes, 2420 is divisible by 242.
Explanation
To confirm if 2420 is divisible by 242:
1) Split the number into two segments: 242 and 0.
2) Check divisibility by the factors of 242 (2, 11, 11).
- 242 is divisible by both 2 and 11.
- 0 is divisible by any number.
3) Since both segments meet the divisibility requirements, 2420 is divisible by 242.
FAQs on Divisibility Rule of 242
1. What is the divisibility rule for 242?
2.How many numbers are there between 1 and 1000 that are divisible by 242?
3. Is 726 divisible by 242?
4. What if I get 0 after the alternating sum for 11?
5.Does the divisibility rule of 242 apply to all integers?
6.How can children in Canada use numbers in everyday life to understand Divisibility Rule of 242?
7.What are some fun ways kids in Canada can practice Divisibility Rule of 242 with numbers?
8.What role do numbers and Divisibility Rule of 242 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Divisibility Rule of 242 skills?
Important Glossaries for Divisibility Rule of 242
- Divisibility rule: The set of rules used to determine whether a number is divisible by another number.
- Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 242 are 242, 484, 726, etc.
- Alternating sum: The sum and difference of digits in alternating sequence used to test divisibility by 11.
- Factors: Numbers that are multiplied together to get another number. For 242, the factors are 2 and 11.
- Even number: A number divisible by 2, having 0, 2, 4, 6, or 8 as the last digit.
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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.
