204 LearnersLast updated on May 26th, 2025
Divisibility Rule of 496
The divisibility rule is a quick way to determine whether a number is divisible by another number without performing the actual division. In practical situations, divisibility rules help in doing quick calculations, distributing things evenly, and organizing items efficiently. In this topic, we will explore the divisibility rule of 496.
What is the Divisibility Rule of 496?
The divisibility rule for 496 is a method by which we can find out if a number is divisible by 496 without using traditional division. Let's check if 992 is divisible by 496 using this rule.
Step 1: Since 496 is a composite number, first check divisibility by its prime factors, which are 2, 2, 2, 31 (since 496 = 2^4 × 31).
Step 2: Check for divisibility by 16 (2^4). The last four digits of the number (0992) should be divisible by 16. 992 ÷ 16 = 62, which is a whole number.
Step 3: Check for divisibility by 31. Use the divisibility rule for 31: Multiply the last digit by 3, add the result to the rest of the number, and check if the sum is a multiple of 31. For 992, multiply the last digit (2) by 3, giving 6, and add this to the rest of the number (99), resulting in 105. 105 ÷ 31 is not a whole number, so 992 is not divisible by 31.
Since 992 is not divisible by 31, it is not divisible by 496 either.
Tips and Tricks for Divisibility Rule of 496
Understanding and mastering the divisibility rules can significantly aid in mathematical calculations. Here are some tips and tricks for the divisibility rule of 496:
- Know the prime factorization: Remember the prime factorization of 496 as 2^4 × 31, which helps check divisibility by smaller components.
- Use divisibility by powers of 2: Learn the rules for divisibility by powers of 2 (e.g., 4, 8, 16) to simplify checking larger numbers.
- Practice the rule for 31: Familiarize yourself with the divisibility rule for 31 to quickly assess larger numbers.
- Repeat the process for large numbers: For large numbers, break them down and check divisibility by smaller factors sequentially.
- Verify using division: After applying the rule, use actual division to verify your results and strengthen your understanding.
Common Mistakes and How to Avoid Them in Divisibility Rule of 496
While using the divisibility rule of 496, common mistakes may occur, leading to incorrect conclusions. Here are some common errors and their solutions:
Mistake 1
Ignoring prime factorization.
Always start by breaking 496 into its prime factors (2^4 × 31) to use the rule effectively.
Mistake 2
Incorrectly applying rules for smaller factors.
Ensure you apply divisibility rules correctly for smaller factors like 16 and 31.
Mistake 3
Confusing the steps.
Practice regularly to memorize the steps involved in checking divisibility by 496.
Mistake 4
Not verifying with actual division.
Cross-check your results using long division to confirm your answer.
Mistake 5
Overlooking negative results.
When working with negative results, treat them as positive for divisibility checks.
Divisibility Rule of 496 Examples
Problem 1
Is 1984 divisible by 496?
Yes, 1984 is divisible by 496.
Explanation
To determine if 1984 is divisible by 496, consider dividing it directly:
1) Divide the number by 496, 1984 ÷ 496 = 4.
2) Since the result is a whole number, 1984 is divisible by 496.
Problem 2
Check if 2480 is divisible by 496.
No, 2480 is not divisible by 496.
Explanation
To check the divisibility of 2480 by 496:
1) Divide the number by 496, 2480 ÷ 496 = 5.
2) Since the division does not result in a whole number, 2480 is not divisible by 496.
Problem 3
Is -992 divisible by 496?
Yes, -992 is divisible by 496.
Explanation
To check divisibility of -992 by 496, ignore the negative sign and divide:
1) Divide the number by 496, 992 ÷ 496 = 2.
2) Since the result is a whole number, -992 is divisible by 496.
Problem 4
Can 594 be divisible by 496?
No, 594 is not divisible by 496.
Explanation
To determine if 594 is divisible by 496:
1) Divide the number by 496, 594 ÷ 496 = 1.2.
2) The division does not result in a whole number, so 594 is not divisible by 496.
Problem 5
Check if 2976 is divisible by 496.
Yes, 2976 is divisible by 496.
Explanation
To verify the divisibility of 2976 by 496:
1) Divide the number by 496, 2976 ÷ 496 = 6.
2) The division results in a whole number, indicating that 2976 is divisible by 496.
FAQs on Divisibility Rule of 496
1.What is the divisibility rule for 496?
2.How do you check if a number is divisible by 16?
3.Is 1488 divisible by 496?
4.What if a number is divisible by 16 but not by 31?
5.Does the divisibility rule of 496 apply to all integers?
6.How can children in Australia use numbers in everyday life to understand Divisibility Rule of 496?
7.What are some fun ways kids in Australia can practice Divisibility Rule of 496 with numbers?
8.What role do numbers and Divisibility Rule of 496 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Divisibility Rule of 496 skills?
Important Glossary for Divisibility Rule of 496
- Divisibility rule: A set of guidelines to determine if one number is divisible by another without performing division.
- Prime factorization: Breaking down a number into its prime number components.
- Composite number: A positive integer with more than two distinct positive divisors.
- Multiples: The result of multiplying one integer by another.
- Integer: A whole number that can be positive, negative, or zero.
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About BrightChamps in Australia
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.
