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121 LearnersLast updated on February 18th, 2025
Divisibility Rule of 998
The divisibility rule is a way to determine whether a number is divisible by another number without performing full division. In real life, we can use divisibility rules for quick calculations, dividing things evenly, and sorting items efficiently. In this topic, we will explore the divisibility rule for 998.
What is the Divisibility Rule of 998?
The divisibility rule for 998 is a method to find out if a number is divisible by 998 without performing division. Let's explore whether 2994 is divisible by 998 using the divisibility rule.
Step 1: Divide the given number into groups of three digits from right to left. In 2994, we have the groups: 2 and 994.
Step 2: Add these groups. Here, 2 + 994 = 996.
Step 3: Check if the sum 996 is a multiple of 998. Since 996 is not a multiple of 998, 2994 is not divisible by 998.
Tips and Tricks for Divisibility Rule of 998
Learning the divisibility rule can help students master division. Here are some tips and tricks for the divisibility rule of 998:
Know the multiples of 998:
Memorize the multiples of 998 (998, 1996, 2994... etc.) to quickly check for divisibility. If the sum of the groups is a multiple of 998, then the number is divisible by 998.
Repeat the process for large numbers:
For large numbers, keep repeating the divisibility process until you reach a sum that is easy to compare with multiples of 998. For example, check if 1996000 is divisible by 998.
- Break into groups of three digits: 1, 996, 000.
- Add the groups: 1 + 996 + 0 = 997.
- Since 997 is not a multiple of 998, 1996000 is not divisible by 998.
Use the division method to verify:
You can use the division method as a way to verify and cross-check your results. This will help confirm your findings and reinforce learning.
Common Mistakes and How to Avoid Them in Divisibility Rule of 998
The divisibility rule of 998 helps us quickly determine if a number is divisible by 998. However, common mistakes like calculation errors can lead to incorrect results. Let's understand some common mistakes and how to avoid them:
Mistake 1
Not grouping the digits correctly.
Ensure you group digits into sets of three from right to left.
Divisibility Rule of 998 Examples
Problem 1
Is 3992 divisible by 998?
Yes, 3992 is divisible by 998.
Explanation
To check if 3992 is divisible by 998:
1) Multiply the last three digits of the number by 2, 992 × 2 = 1984.
2) Subtract the result from the remaining digits excluding the last three digits, 3 – 1984 = -1981.
3) Since -1981 is not 0 and is not a multiple of 998, let's recheck our calculation. Correcting the calculation: 3 - 1984 results in -1981, which should have been interpreted differently. Let's multiply the last section by 4 instead to check another divisibility rule: 992 × 4 = 3968.
4) Subtract from the initial part, 4000 - 3968 = 32.
5) Since the adjusted subtraction leads to a smaller number, we can check the division: 3992 ÷ 998 = 4, which gives a whole number; hence 3992 is divisible by 998.
Problem 2
Check the divisibility rule of 998 for 2994.
No, 2994 is not divisible by 998.
Explanation
For checking if 2994 is divisible by 998:
1) Multiply the last three digits by 2, 994 × 2 = 1988.
2) Subtract the result from the remaining digits, 2 - 1988 = -1986.
3) Since -1986 is not 0, check the direct division: 2994 ÷ 998 = 3, with a remainder, indicating 2994 is not divisible by 998.
Problem 3
Is -1996 divisible by 998?
Yes, -1996 is divisible by 998
Explanation
To check if -1996 is divisible by 998, remove the negative sign and check the divisibility of 1996:
1) Multiply the last three digits by 2, 996 × 2 = 1992.
2) Subtract the result from the remaining digits, 1 - 1992 = -1991.
3) Since -1991 does not simplify directly, check: 1996 ÷ 998 = 2, which gives a whole number; hence -1996 is divisible by 998.
Problem 4
Can 1001 be divisible by 998 following the divisibility rule?
No, 1001 isn't divisible by 998.
Explanation
To check if 1001 is divisible by 998, follow these steps:
1) Multiply the last three digits by 2, 001 × 2 = 2.
2) Subtract the result from the remaining digits, 1 - 2 = -1.
3) Check if -1 is a multiple of 998. No, -1 is not a multiple of 998, verifying 1001 isn't divisible by 998.
Problem 5
Check the divisibility rule of 998 for 9978.
Yes, 9978 is divisible by 998.
Explanation
To check if 9978 is divisible by 998:
1) Multiply the last three digits by 2, 978 × 2 = 1956.
2) Subtract the result from the remaining digits, 9 - 1956 = -1947.
3) Recalculate for clarity: 9978 ÷ 998 = 10, which gives a whole number, confirming divisibility.
FAQs on Divisibility Rule of 998
1. What is the divisibility rule for 998?
2.How many numbers are there between 1 and 100 that are divisible by 998?
3.Is 2994 divisible by 998?
4.What if I get 0 after adding the groups?
5.Does the divisibility rule of 998 apply to all integers?
Important Glossaries for Divisibility Rule of 998
- Divisibility Rule: A set of rules used to determine whether a number is divisible by another number without performing full division.
- Multiples: Numbers that are the result of multiplying a given number by an integer. For example, multiples of 998 are 998, 1996, 2994, etc.
- Integer: A whole number that can be positive, negative, or zero.
- Grouping: The process of dividing a number into sets of digits, typically for simplifying operations like the divisibility rule.
- Verification: The process of confirming the accuracy of a result, often by using an alternative method like direct division.
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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.
