Answer The Questions Below. Be Sure To Mark All Answers That Apply.$[ \begin{array}{|l|c|c|c|c|} \hline & & 634 & 932 & 415 \ \hline \text{None Of These} & & \square & \square & \square & \square \ \hline (a) \text{Which Numbers Are Divisible By
Introduction
In mathematics, divisibility is a fundamental concept that deals with the relationship between numbers and their factors. It is essential to understand the rules of divisibility to solve various mathematical problems and puzzles. In this article, we will explore the concept of divisibility and answer some questions related to it.
What are the Rules of Divisibility?
The rules of divisibility are based on the factors of a number. A number is divisible by another number if the latter is a factor of the former. For example, 6 is divisible by 2 and 3 because 2 and 3 are factors of 6.
Which Numbers are Divisible by 2?
A number is divisible by 2 if its last digit is even, i.e., 0, 2, 4, 6, or 8. In the given table, the numbers 634 and 932 are divisible by 2 because their last digits are 4 and 2, respectively.
Which Numbers are Divisible by 3?
A number is divisible by 3 if the sum of its digits is divisible by 3. In the given table, the numbers 634 and 415 are divisible by 3 because the sum of their digits is 19 and 13, respectively, which are not divisible by 3. However, the number 932 is not divisible by 3 because the sum of its digits is 13, which is not divisible by 3.
Which Numbers are Divisible by 5?
A number is divisible by 5 if its last digit is 0 or 5. In the given table, the number 415 is divisible by 5 because its last digit is 5.
Which Numbers are Divisible by 7?
A number is divisible by 7 if the difference between twice the digit at the units place and the number formed by the remaining digits is divisible by 7. In the given table, none of the numbers are divisible by 7.
Which Numbers are Divisible by 11?
A number is divisible by 11 if the difference between the sum of the digits at odd places and the sum of the digits at even places is divisible by 11. In the given table, none of the numbers are divisible by 11.
Conclusion
In conclusion, the rules of divisibility are based on the factors of a number. A number is divisible by another number if the latter is a factor of the former. We have explored the concept of divisibility and answered some questions related to it. We have also discussed the divisibility rules for numbers 2, 3, 5, 7, and 11.
Divisibility Rules Summary
| Number | Divisible by 2 | Divisible by 3 | Divisible by 5 | Divisible by 7 | Divisible by 11 |
|---|---|---|---|---|---|
| 634 | |||||
| 932 | |||||
| 415 |
Answer Key
- 634: None of these
- 932: None of these
- 415: None of these
Introduction
In our previous article, we explored the concept of divisibility in mathematics and discussed the rules of divisibility for numbers 2, 3, 5, 7, and 11. In this article, we will provide a Q&A guide to help you understand the concept of divisibility better.
Q: What is Divisibility?
A: Divisibility is a fundamental concept in mathematics that deals with the relationship between numbers and their factors. A number is divisible by another number if the latter is a factor of the former.
Q: How do I Determine if a Number is Divisible by 2?
A: To determine if a number is divisible by 2, you need to check if its last digit is even, i.e., 0, 2, 4, 6, or 8. If the last digit is even, then the number is divisible by 2.
Q: How do I Determine if a Number is Divisible by 3?
A: To determine if a number is divisible by 3, you need to check if the sum of its digits is divisible by 3. If the sum of the digits is divisible by 3, then the number is divisible by 3.
Q: How do I Determine if a Number is Divisible by 5?
A: To determine if a number is divisible by 5, you need to check if its last digit is 0 or 5. If the last digit is 0 or 5, then the number is divisible by 5.
Q: How do I Determine if a Number is Divisible by 7?
A: To determine if a number is divisible by 7, you need to check if the difference between twice the digit at the units place and the number formed by the remaining digits is divisible by 7. If the difference is divisible by 7, then the number is divisible by 7.
Q: How do I Determine if a Number is Divisible by 11?
A: To determine if a number is divisible by 11, you need to check if the difference between the sum of the digits at odd places and the sum of the digits at even places is divisible by 11. If the difference is divisible by 11, then the number is divisible by 11.
Q: What are the Divisibility Rules for Numbers 4, 6, 8, 9, and 10?
A: The divisibility rules for numbers 4, 6, 8, 9, and 10 are as follows:
- A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
- A number is divisible by 6 if it is divisible by both 2 and 3.
- A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
- A number is divisible by 9 if the sum of its digits is divisible by 9.
- A number is divisible by 10 if its last digit is 0.
Q: How do I Use the Divisibility Rules to Solve Problems?
A: To use the divisibility rules to solve problems, you need to apply the rules to the numbers involved in the problem. For example, if you are asked to determine if a number is divisible by 3, you need to check if the sum of its digits is divisible by 3.
Conclusion
In conclusion, the divisibility rules are a set of guidelines that help you determine if a number is divisible by another number. By understanding the divisibility rules, you can solve various mathematical problems and puzzles. We hope that this Q&A guide has helped you understand the concept of divisibility better.
Divisibility Rules Summary
| Number | Divisible by 2 | Divisible by 3 | Divisible by 5 | Divisible by 7 | Divisible by 11 |
|---|---|---|---|---|---|
| 634 | |||||
| 932 | |||||
| 415 |
Answer Key
- 634: None of these
- 932: None of these
- 415: None of these