189 LearnersLast updated on May 26th, 2025
Divisibility Rule of 196
The divisibility rule is a way to determine whether a number is divisible by another number without performing division. In real life, these rules can help with quick math, dividing things evenly, and sorting items. In this topic, we will explore the divisibility rule of 196.
What is the Divisibility Rule of 196?
The divisibility rule for 196 allows us to determine if a number is divisible by 196 without performing actual division. Let's check if 1372 is divisible by 196 using the divisibility rule.
Step 1: Break down the number into smaller parts or use known rules for constituent factors of 196, such as 4 and 49 (since 196 = 4 × 49).
Step 2: Apply divisibility rules for each factor separately. For instance, check if 1372 is divisible by 4 and 49.
Divisibility by 4: A number is divisible by 4 if the last two digits form a number divisible by 4. In 1372, the last two digits are 72, which is divisible by 4.
Divisibility by 49: A number is divisible by 49 if the difference between twice the hundreds digit and the rest of the number is a multiple of 49. Here, twice the hundreds digit is 2×13=26, and the remaining number is 72. The difference 72-26=46 is not a multiple of 49, so 1372 is not divisible by 49.
Step 3: Since 1372 is not divisible by 49, it is not divisible by 196.
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Tips and Tricks for Divisibility Rule of 196
Understanding divisibility rules can help students master division. Here are some tips and tricks for the divisibility rule of 196:
- Know the factors of 196: Recognize that 196 is 4×49. Check divisibility by both factors.
- Use smaller divisibility rules: Apply the divisibility rules for 4 and 49 separately to simplify the process.
- Repeat the process for large numbers: For larger numbers, break down the problem into manageable steps by verifying divisibility by smaller factors.
- Use the division method to verify: Verify results with actual division to ensure accuracy.
Common Mistakes and How to Avoid Them in Divisibility Rule of 196
The divisibility rule of 196 helps us quickly check if a number is divisible by 196. However, common mistakes can occur, leading to incorrect conclusions. Here are some common errors and solutions:
Mistake 1
Ignoring the need to check both factors.
Remember that 196=4×49, so check divisibility by both 4 and 49.
Mistake 2
Misapplying divisibility rules for constituent factors.
Ensure correct application of the divisibility rules for 4 and 49.
Mistake 3
Not repeating the process for larger numbers.
Break down complex numbers and check smaller parts.
Mistake 4
Overlooking negative results.
Consider the absolute value when checking divisibility.
Mistake 5
Confusing steps for different factors.
Practice regularly to avoid confusion between steps for 4 and 49.
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Divisibility Rule of 196 Examples
Problem 1
Is 392 divisible by 196?
Yes, 392 is divisible by 196.
Explanation
To check if 392 is divisible by 196:
1) Recognize that 196 is 14 squared. Check if 392 can be evenly divided by 14 first.
2) 392 divided by 14 equals 28, which is an integer.
3) Since 28 is an integer, we can divide it by 14 again to check if 392 is divisible by 196.
4) 28 divided by 14 equals 2, which is an integer.
5) Therefore, 392 is divisible by 196.
Problem 2
Check the divisibility rule of 196 for 588.
Yes, 588 is divisible by 196.
Explanation
To verify if 588 is divisible by 196:
1) Recognize that 196 is 14 squared. Check if 588 is divisible by 14.
2) 588 divided by 14 equals 42, which is an integer.
3) Now, divide 42 by 14 to confirm divisibility by 196.
4) 42 divided by 14 equals 3, which is an integer.
5) Therefore, 588 is divisible by 196.
Problem 3
Is 980 divisible by 196?
No, 980 is not divisible by 196.
Explanation
To determine if 980 is divisible by 196:
1) Check if 980 is divisible by 14 first.
2) 980 divided by 14 equals 70, which is an integer.
3) Next, check if 70 is divisible by 14.
4) 70 divided by 14 equals 5, which is an integer.
5) Thus, 980 is divisible by 14 squared (196) since both steps resulted in integers.
Problem 4
Can 1232 be divisible by 196 following the divisibility rule?
Yes, 1232 is divisible by 196.
Explanation
To check if 1232 is divisible by 196:
1) Check if 1232 can be divided by 14.
2) 1232 divided by 14 equals 88, which is an integer.
3) Then, check if 88 is divisible by 14.
4) 88 divided by 14 equals 6.2857, which is not an integer.
5) Therefore, 1232 is not divisible by 196 as the final division gave a non-integer value.
Problem 5
Check the divisibility rule of 196 for 1764.
Yes, 1764 is divisible by 196.
Explanation
To verify if 1764 is divisible by 196:
1) Check if 1764 is divisible by 14.
2) 1764 divided by 14 equals 126, which is an integer.
3) Then check if 126 is divisible by 14.
4) 126 divided by 14 equals 9, which is an integer.
5) Therefore, 1764 is divisible by 196, as both divisions resulted in integers.
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FAQs on Divisibility Rule of 196
1.What is the divisibility rule for 196?
2.How can I check if a number is divisible by 49?
3.Is 392 divisible by 196?
4.What if I get a negative number after subtraction?
5.Does the divisibility rule of 196 apply to all integers?
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Important Glossaries for Divisibility Rule of 196
- Divisibility rule: A set of guidelines to determine if a number can be divided by another without remainder.
- Factors: Numbers that multiply together to produce another number. For 196, they are 4 and 49.
- Multiples: The result of multiplying a number by an integer. For example, multiples of 196 include 196, 392, 588, etc.
- Integers: Whole numbers that can be positive, negative, or zero.
- Subtraction: The process of finding the difference between two numbers.
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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.
