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120 LearnersLast updated on February 16th, 2025
Divisibility Rule of 661
The divisibility rule is a way to find out whether a number is divisible by another number without using the division method. In real life, we can use the divisibility rule for quick math, dividing things evenly, and sorting things. In this topic, we will learn about the divisibility rule of 661.
What is the Divisibility Rule of 661?
The divisibility rule for 661 is a method by which we can find out if a number is divisible by 661 or not without using the division method.
Check whether 1983 is divisible by 661 with the divisibility rule.
Step 1: Multiply the last digit of the number by 2, here in 1983, 3 is the last digit, so multiply it by 2. 3 × 2 = 6
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 198–6 = 192.
Step 3: As it is shown that 192 is not a multiple of 661, the number is not divisible by 661. If the result from step 2 isn't a multiple of 661, then the number isn't divisible by 661.
Tips and Tricks for Divisibility Rule of 661
Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 661.
- Know the multiples of 661: Memorize the multiples of 661 (661, 1322, 1983, 2644, 3305…etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 661, then the number is divisible by 661.
- Use the negative numbers: If the result we get after the subtraction is negative, we will avoid the symbol and consider it as positive for checking the divisibility of a number.
- Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 661.
For example: Check if 5943 is divisible by 661 using the divisibility test.Multiply the last digit by 2, i.e., 3 × 2 = 6Subtract the remaining digits excluding the last digit by 6, 594–6 = 588
Still, 588 is a large number, hence we will repeat the process again and multiply the last digit by 2, 8 × 2 = 16.
Now subtracting 16 from the remaining numbers excluding the last digit, 58–16 = 42
As 42 is not a multiple of 661, 5943 is not divisible by 661.
- Use the division method to verify: Students can use the division method as a way to verify and crosscheck their results. This will help them to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 661
The divisibility rule of 661 helps us to quickly check if the given number is divisible by 661, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes that will help you to understand.
Mistake 1
Not following the correct steps.
Students should follow the correct steps that are multiplying the last digit by 2 and then subtracting the result from the remaining digits excluding the last digit and checking whether it is a multiple of 661.
Divisibility Rule of 661 Examples
Problem 1
Is 1983 divisible by 661?
Yes, 1983 is divisible by 661.
Explanation
To check if 1983 is divisible by 661, we use the divisibility concept specific to 661.
1) Break 1983 into parts related to 661, such as 1983 = 3 × 661.
2) Verify multiplication: 3 × 661 = 1983.
3) Since 1983 is exactly 3 times 661, it is divisible by 661.
Problem 2
Check the divisibility rule of 661 for 2644.
Yes, 2644 is divisible by 661.
Explanation
To determine this, we look at how many times 661 fits into 2644.
1) Divide 2644 by 661: 2644 ÷ 661 = 4.
2) Verify multiplication: 4 × 661 = 2644.
3) Since the division results in a whole number, 2644 is divisible by 661.
Problem 3
Is 1322 divisible by 661?
Yes, 1322 is divisible by 661.
Explanation
We need to check if 1322 can be expressed as a multiple of 661.
1) Divide 1322 by 661: 1322 ÷ 661 = 2.
2) Verify multiplication: 2 × 661 = 1322.
3) The exact division confirms that 1322 is divisible by 661.
Problem 4
Can 1984 be divisible by 661 following the divisibility rule?
No, 1984 is not divisible by 661.
Explanation
To verify, we attempt to divide 1984 by 661.
1) Divide 1984 by 661: 1984 ÷ 661 ≈ 3.002.
2) Since the result is not a whole number, 1984 is not divisible by 661.
Problem 5
Check the divisibility rule of 661 for 3305.
Yes, 3305 is divisible by 661.
Explanation
We verify by checking the multiple.
1) Divide 3305 by 661: 3305 ÷ 661 = 5.
2) Verify multiplication: 5 × 661 = 3305.
3) As the division yields a whole number, 3305 is divisible by 661.
FAQs on Divisibility Rule of 661
1.What is the divisibility rule for 661?
2.How many numbers are there between 1 and 1000 that are divisible by 661?
3.Is 2644 divisible by 661?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 661 apply to all the integers?
Important Glossaries for Divisibility Rule of 661
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not. For example, a number is divisible by 661 if the final result after applying the rule is a multiple of 661.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example: multiples of 661 are 661, 1322, 1983, 2644, etc.
- Integers: Integers are the numbers that include all the whole numbers, negative numbers, and zero.
- Subtraction: Subtraction is a process of finding out the difference between two numbers, by reducing one number from another.
- Verification: Verification is the process of confirming a result, often using a different method like direct division to check if a number is divisible by another.
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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.
