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116 LearnersLast updated on February 18th, 2025
Divisibility Rule of 921
The divisibility rule is a method to determine whether a number is divisible by another number without performing the division operation. In real life, divisibility rules allow for quick calculations, even distribution, and organization. In this topic, we will explore the divisibility rule of 921.
What is the Divisibility Rule of 921?
The divisibility rule for 921 is a method by which we can determine if a number is divisible by 921 without division. Let's check whether 1842 is divisible by 921 using this rule.
Step 1: Multiply the last digit of the number by 2. In 1842, the last digit is 2. Multiply it by 2: 2 × 2 = 4.
Step 2: Add the result from Step 1 to the remaining number, excluding the last digit. That is, 184 + 4 = 188.
Step 3: Since 188 is not a multiple of 921, 1842 is not divisible by 921. If the result from Step 2 were a multiple of 921, the number would be divisible by 921.
Tips and Tricks for Divisibility Rule of 921
Learning the divisibility rule helps students master division. Here are a few tips and tricks for the divisibility rule of 921:
Know the multiples of 921:
Memorize the multiples of 921 (921, 1842, 2763, etc.) to quickly check divisibility. If the result from the addition is a multiple of 921, then the number is divisible by 921.
Use negative numbers:
If the result after addition is negative, treat it as positive to check divisibility.
Repeat the process for large numbers:
Continue the divisibility process until reaching a smaller number divisible by 921. For example, check if 3684 is divisible by 921:
Multiply the last digit by 2, i.e., 4 × 2 = 8.
Add the remaining digits excluding the last digit, 368 + 8 = 376.
Since 376 is not a multiple of 921, 3684 is not divisible by 921.
Use the division method to verify:
Students can use the division method to verify their results, reinforcing their learning.
Common Mistakes and How to Avoid Them in Divisibility Rule of 921
The divisibility rule of 921 helps quickly determine if a number is divisible by 921. Here are common mistakes and solutions:
Mistake 1
Not following the correct steps.
Follow the correct steps: multiply the last digit by 2, add the result to the remaining digits, and check if it is a multiple of 921.
Divisibility Rule of 921 Examples
Problem 1
Is 3684 divisible by 921?
Yes, 3684 is divisible by 921.
Explanation
To determine if 3684 is divisible by 921, we can use a hypothetical divisibility rule:
1) Divide the number into chunks of 3 digits from the right, which gives us 3 and 684.
2) Consider the chunks as separate numbers, 3 is a part of 3000, and 684 remains.
3) Check if these parts are both divisible by 921. Here, 3000 and 684 individually don't satisfy the condition but their sum, 3684, is divisible by 921 as a whole.
Problem 2
Check the divisibility rule of 921 for 5526.
No, 5526 is not divisible by 921.
Explanation
Let's apply a hypothetical rule for divisibility by 921:
1) Break the number into sections of three digits from the right, resulting in 5 and 526.
2) Analyze each section—5 can be part of 5000, and 526.
3) If neither section is divisible by 921, the entire number isn't. Here, neither 5000 nor 526 is divisible by 921, so 5526 is not divisible by 921.
Problem 3
Is -921 divisible by 921?
Yes, -921 is divisible by 921.
Explanation
For a negative number, we first consider its absolute value:
1) The absolute value of -921 is 921.
2) Check if 921 is divisible by itself.
3) Since any number is divisible by itself, -921 divided by 921 results in -1, confirming divisibility.
Problem 4
Can 1842 be divisible by 921 following a divisibility rule?
Yes, 1842 is divisible by 921.
Explanation
To verify this, let's use an imagined rule for checking divisibility by 921:
1) Consider the number 1842, which can be split into 1 and 842.
2) These parts, when added together, give 1842.
3) Check if 1842 is a multiple of 921, and indeed, 921 multiplied by 2 gives 1842.
Problem 5
Check the divisibility rule of 921 for 2763.
Yes, 2763 is divisible by 921.
Explanation
Using a hypothetical check for divisibility by 921:
1) Divide the number into segments of three digits from the right, yielding 2 and 763.
2) Consider these sections together to see if they sum to a multiple of 921.
3) 2763 is indeed a multiple of 921, as 921 x 3 equals 2763.
FAQs on Divisibility Rule of 921
1.What is the divisibility rule for 921?
2.How many numbers between 1 and 10,000 are divisible by 921?
3. Is 1842 divisible by 921?
4.What if I get 0 after adding?
5.Does the divisibility rule of 921 apply to all integers?
Important Glossaries for Divisibility Rule of 921:
- Divisibility rule: A set of guidelines to determine if a number is divisible by another number without performing division.
- Multiples: The results obtained by multiplying a number by an integer. For example, multiples of 921 are 921, 1842, 2763, etc.
- Integers: Numbers that include all whole numbers, negative numbers, and zero.
- Addition: The process of calculating the total of two or more numbers or amounts.
- Subtraction: The process of determining the difference between two numbers by reducing one from 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.
