Divisibility tests are essential tools in mathematics, offering shortcuts to determine if one number is divisible by another. additionally, divisibility tests helps students manage swift mathematical operations in their daily in class and out of class operations. Thus, this comprehensive blog delves into the divisibility test of 6, 8, and 9, providing practical illustrations, solving problems, and guiding learners through the process of testing divisibility. Therefore, by the end of this exploration, you will gain a solid understanding of divisibility tests of 6, 8, and 9, empowering you to apply this knowledge confidently in various mathematical contexts.
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Unveiling Divisiblity of 6, 8, and 9
- Understanding Divisibility Tests:
Divisibility tests provide shortcuts to determine if one number is divisible by another without performing division. For numbers 6, 8, and 9, specific rules apply to test their divisibility.
- Divisibility by 6:
A number is divisible by 6 if it is divisible by both 2 and 3. This means that the number must be even and the sum of its digits must be divisible by 3.
- Divisibility by 8:
A number is divisible by 8 if the number formed by its last three digits is divisible by 8. This test applies to larger numbers, where only the last three digits are considered.
- Divisibility by 9:
A number is divisible by 9 if the sum of its digits is divisible by 9. This test is similar to the test for divisibility by 3, but it applies to divisibility by 9.
- Practical Illustrations:
- 1. Divisibility Test for 6:
Let’s test the number 144 for divisibility by 6. Since it is even and the sum of its digits is 1 + 4 + 4 = 9, which is divisible by 3, 144 is divisible by 6.
- 2. Divisibility Test for 8:
Consider the number 1,328. The number formed by its last three digits is 328, which is not divisible by 8. Therefore, 1,328 is not divisible by 8.
- 3. Divisibility Test for 9:
Take the number 837. The sum of its digits is 8 + 3 + 7 = 18, which is divisible by 9. Therefore, 837 is divisible by 9.
Solving Problems Involving Divisibility test of 6, 8, and 9:
Let’s tackle some word problems involving divisibility tests:
- 1. Problem 1:
Determine if 252 is divisible by 6.
Solution: Since it is even and the sum of its digits is \( 2 + 5 + 2 = 9 \), which is divisible by 3, 252 is divisible by 6.
- 2. Problem 2:
Is 1,648 divisible by 8?
Solution: The number formed by its last three digits is 648, which is divisible by 8. Therefore, 1,648 is divisible by 8.
Illustrating Divisibility Tests:
- 1. Divisibility Test for 6:
-Check if the number is even.
-Determine if the sum of its digits is divisible by 3.
- 2. Divisibility Test for 8:
-Consider the last three digits of the number.
-Determine if this number is divisible by 8.
- 3. Divisibility Test for 9:
-Calculate the sum of the digits.
-Check if this sum is divisible by 9.
Conclusion:
In conclusion, mastering divisibility tests for numbers 6, 8, and 9 is essential for understanding the properties and relationships of numbers. Hence, by learning these tests, solving problems, and exploring practical illustrations, individuals enhance their mathematical fluency and problem-solving skills. Therefore, let’s embrace the power of divisibility tests, armed with the knowledge and skills to navigate the world of mathematics with confidence and precision.
So, the next time you encounter a number, remember to apply divisibility tests to unravel its properties and relationships, empowering yourself to tackle mathematical challenges with ease and proficiency.
