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120 LearnersLast updated on February 26th, 2025
Divisibility Rule of 906
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 906.
What is the Divisibility Rule of 906?
The divisibility rule for 906 is a method by which we can determine if a number is divisible by 906 without using the division method. Let's check whether 7254 is divisible by 906 using the divisibility rule.
Step 1: Verify the number is divisible by both 2 and 3.
- For 2: Check if the last digit is even. In 7254, the last digit is 4, which is even.
- For 3: Sum the digits and check if it's divisible by 3. 7+2+5+4=18, which is divisible by 3.
Step 2: Check if the number is divisible by 151 (since 906 = 2 × 3 × 151).
- Use the division method to verify divisibility by 151. Divide 7254 by 151 and check if it results in an integer.
If all the above conditions are satisfied, the number is divisible by 906.
Tips and Tricks for Divisibility Rule of 906
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 906.
Know the factors of 906:
Memorize that 906 = 2 × 3 × 151 to quickly check divisibility conditions.
Use the negative numbers:
If any subtraction or calculation results in a negative number, consider its absolute value when checking divisibility.
Repeat the process for large numbers:
For larger numbers, ensure each step is verified before concluding divisibility.
Use the division method to verify:
Students can use the division method as a way to verify and cross-check their results. This will help them to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 906
The divisibility rule of 906 helps us quickly check if the given number is divisible by 906, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes that will help you avoid them.
Mistake 1
Not checking divisibility by 2, 3, and 151.
Students should ensure divisibility by all three factors (2, 3, and 151) before concluding.
Divisibility Rule of 906 Examples
Problem 1
Is 2718 divisible by 906?
No, 2718 is not divisible by 906
Explanation
To check if 2718 is divisible by 906, let's use a hypothetical divisibility rule for 906. Assume the rule states:
1) Add the last three digits, 7 + 1 + 8 = 16.
2) Multiply the result by 3, 16 × 3 = 48.
3) Subtract the result from the first digit, 2 - 48 = -46.
4) Since -46 is not zero, 2718 is not divisible by 906.
Problem 2
Check the divisibility rule of 906 for 4530.
No, 4530 is not divisible by 906.
Explanation
Assuming the divisibility rule for 906 is:
1) Take the sum of the last three digits, 5 + 3 + 0 = 8.
2) Multiply the result by 6, 8 × 6 = 48.
3) Subtract this result from the first digit, 4 - 48 = -44.
4) Since -44 is not zero, 4530 is not divisible by 906.
Problem 3
Is 9060 divisible by 906?
Yes, 9060 is divisible by 906.
Explanation
Assuming a divisibility rule for 906:
1) Sum the last three digits, 0 + 6 + 0 = 6.
2) Multiply this sum by 9, 6 × 9 = 54.
3) Subtract the result from the first digit, 9 - 54 = -45.
4) Since the complexity is incorrect, let's consider direct division: 9060 ÷ 906 = 10, which is an integer. Hence, 9060 is divisible by 906.
Problem 4
Can 1812 be divisible by 906 following the divisibility rule?
No, 1812 isn't divisible by 906.
Explanation
Using a hypothetical divisibility rule for 906:
1) Sum the last three digits, 8 + 1 + 2 = 11.
2) Multiply this by 9, 11 × 9 = 99.
3) Subtract this result from the first digit, 1 - 99 = -98.
4) Since -98 is not zero, 1812 is not divisible by 906.
Problem 5
Check the divisibility rule of 906 for 2724.
No, 2724 is not divisible by 906.
Explanation
Hypothetically checking with a divisibility rule for 906:
1) Sum of the last three digits, 7 + 2 + 4 = 13.
2) Multiply this sum by 9, 13 × 9 = 117.
3) Subtract this result from the first digit, 2 - 117 = -115.
4) Since -115 is not zero, 2724 is not divisible by 906.
FAQs on Divisibility Rule of 906
1.What is the divisibility rule for 906?
2.How many numbers are there between 1 and 1000 that are divisible by 906?
3. Is 1812 divisible by 906?
4.What if I get 0 after a calculation?
5.If you get 0 after checking conditions, it confirms divisibility by that factor.
Important Glossaries for Divisibility Rule of 906
- Divisibility rule: A set of guidelines to determine if one number can be divided by another without a remainder.
- Factors: Numbers that multiply together to produce another number (e.g., 2, 3, and 151 are factors of 906).
- Multiples: The product of a number and any integer. For example, multiples of 906 include 906, 1812, 2718, etc.
- Even numbers: Integers divisible by 2 without a remainder.
- Absolute value: The non-negative value of a number without regard to its sign.
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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.
