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116 LearnersLast updated on February 26th, 2025
Divisibility Rule of 909
The divisibility rule is a way to determine whether a number is divisible by another number without performing the actual division. In real life, we can use divisibility rules for quick calculations, dividing things evenly, and sorting items. In this topic, we will learn about the divisibility rule of 909.
What is the Divisibility Rule of 909?
The divisibility rule for 909 is a method by which we can determine if a number is divisible by 909 without performing division. Let's check whether 2727 is divisible by 909 using this rule.
Step 1: Check if the number is divisible by 3 and 303. If both conditions are met, the number is divisible by 909.
- For 3: Add up all the digits of the number. If the sum is divisible by 3, then the number is divisible by 3. For 2727, 2+7+2+7=18, and 18 is divisible by 3.
- For 303: Check if the number is divisible by 101 (since 303=3×101). Use the divisibility rule of 101 on the same number. If it works, the number is divisible by 303.
Step 2: If 2727 is divisible by both 3 and 303, then it is divisible by 909
Tips and Tricks for Divisibility Rule of 909
Learning the divisibility rule will help students master division. Let’s explore some tips and tricks for the divisibility rule of 909.
Know the factors:
Understand that 909=3×303. A number must be divisible by both 3 and 303 to be divisible by 909.
Use the sum of digits:
As mentioned, summing the digits helps quickly check divisibility by 3.
Check for divisibility by 101:
To verify divisibility by 303, use the rule for 101. If this condition is met, then check further for 303.
Use the division method to verify:
Students can use the division method to verify and cross-check their results. This will help them confirm and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 909
The divisibility rule of 909 helps us quickly check if a given number is divisible by 909, but common mistakes like calculation errors can lead to incorrect conclusions. Here we will address some common errors and how to avoid them.
Mistake 1
Not checking all conditions.
Ensure you check divisibility by both 3 and 303 separately.
Divisibility Rule of 909 Examples
Problem 1
Is 2727 divisible by 909?
Yes, 2727 is divisible by 909.
Explanation
To check if 2727 is divisible by 909, we can use the divisibility rule for 909.
1) Split the number into segments of 3 digits from the right, so we get 2 and 727.
2) Check if the sum of these numbers (2 + 727 = 729) is divisible by 909.
3) 729 is not divisible by 909, so we made an error in steps. Instead, check directly: 2727 ÷ 909 = 3 (exact division), hence 2727 is divisible by 909.
Problem 2
Check the divisibility rule of 909 for 9090.
Yes, 9090 is divisible by 909.
Explanation
For checking the divisibility of 9090 by 909:
1) Break the number into parts of three digits from the right, so we have 9 and 090.
2) Check if the sum of these numbers (9 + 90 = 99) is divisible by 909.
3) 9090 ÷ 909 = 10, which confirms that 9090 is divisible by 909.
Problem 3
Is -1818 divisible by 909?
Yes, -1818 is divisible by 909.
Explanation
To check if -1818 is divisible by 909, remove the negative sign:
1) Divide the number 1818 by 909.
2) 1818 ÷ 909 = 2, which is a whole number, indicating divisibility.
3) Hence, -1818 is divisible by 909.
Problem 4
Can 1234 be divisible by 909 following the divisibility rule?
No, 1234 isn't divisible by 909.
Explanation
To check if 1234 is divisible by 909:
1) Attempt to divide 1234 by 909.
2) 1234 ÷ 909 ≈ 1.357, which is not a whole number.
3) Therefore, 1234 is not divisible by 909.
Problem 5
Check the divisibility rule of 909 for 1818.
Yes, 1818 is divisible by 909.
Explanation
To check the divisibility of 1818 by 909:
1) Divide the number directly: 1818 ÷ 909 = 2.
2) Since the result is a whole number, 1818 is divisible by 909.
FAQs on Divisibility Rule of 909
1.What is the divisibility rule for 909?
2.How do you check if a number is divisible by 3?
3.How many numbers between 1 and 1000 are divisible by 909?
4.Is 909 divisible by 909?
5.Does the divisibility rule of 909 apply to negative integers?
Important Glossaries for Divisibility Rule of 909
- Divisibility rule: A set of rules used to determine whether a number is divisible by another number without performing division.
- Factors: Numbers that multiply together to produce another number. For 909, the factors are 3 and 303.
- Sum of digits: Adding all the digits of a number to check for divisibility by certain numbers, such as 3.
- Integer: A whole number that can be positive, negative, or zero.
- Verification: The process of confirming the result using an alternative method, such as 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.
