Answer The Questions Below. Be Sure To Mark All Answers That Apply.$[ \begin{array}{|l|c|c|c|c|} \hline & 444 & 530 & 195 & \text{None Of These} \ \hline \text{(a) Which Numbers Are Divisible By 2?} & \square & \square & \square & \square

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Introduction

Mathematics is a vast and fascinating subject that deals with numbers, quantities, and shapes. It is a fundamental tool for problem-solving, critical thinking, and logical reasoning. In this article, we will explore a set of questions related to mathematics and provide step-by-step answers to each of them.

Question 1: Which numbers are divisible by 2?

To answer this question, we need to understand what it means for a number to be divisible by 2. A number is divisible by 2 if it can be divided by 2 without leaving a remainder.

  • 444: We can divide 444 by 2 without leaving a remainder, so it is divisible by 2.
  • 530: We cannot divide 530 by 2 without leaving a remainder, so it is not divisible by 2.
  • 195: We cannot divide 195 by 2 without leaving a remainder, so it is not divisible by 2.
  • None of these: This option is not applicable, as we have already identified the numbers that are divisible by 2.

Therefore, the correct answer is 444.

Question 2: Which numbers are divisible by 5?

To answer this question, we need to understand what it means for a number to be divisible by 5. A number is divisible by 5 if it can be divided by 5 without leaving a remainder.

  • 444: We cannot divide 444 by 5 without leaving a remainder, so it is not divisible by 5.
  • 530: We can divide 530 by 5 without leaving a remainder, so it is divisible by 5.
  • 195: We can divide 195 by 5 without leaving a remainder, so it is divisible by 5.
  • None of these: This option is not applicable, as we have already identified the numbers that are divisible by 5.

Therefore, the correct answers are 530 and 195.

Question 3: Which numbers are even?

To answer this question, we need to understand what it means for a number to be even. An even number is a number that can be divided by 2 without leaving a remainder.

  • 444: We can divide 444 by 2 without leaving a remainder, so it is even.
  • 530: We cannot divide 530 by 2 without leaving a remainder, so it is not even.
  • 195: We cannot divide 195 by 2 without leaving a remainder, so it is not even.
  • None of these: This option is not applicable, as we have already identified the numbers that are even.

Therefore, the correct answer is 444.

Question 4: Which numbers are odd?

To answer this question, we need to understand what it means for a number to be odd. An odd number is a number that cannot be divided by 2 without leaving a remainder.

  • 444: We can divide 444 by 2 without leaving a remainder, so it is not odd.
  • 530: We cannot divide 530 by 2 without leaving a remainder, so it is odd.
  • 195: We cannot divide 195 by 2 without leaving a remainder, so it is odd.
  • None of these: This option is not applicable, as we have already identified the numbers that are odd.

Therefore, the correct answers are 530 and 195.

Conclusion

In this article, we have answered a set of questions related to mathematics. We have identified the numbers that are divisible by 2, 5, even, and odd. We have also provided step-by-step explanations for each of the questions. We hope that this article has provided valuable insights and knowledge to our readers.

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Introduction

Welcome to our Q&A article on mathematics and divisibility. In this article, we will answer some of the most frequently asked questions related to mathematics and divisibility. Whether you are a student, a teacher, or simply someone who is interested in mathematics, this article is for you.

Q1: What is mathematics?

A1: Mathematics is a branch of science that deals with numbers, quantities, and shapes. It is a fundamental tool for problem-solving, critical thinking, and logical reasoning.

Q2: What is divisibility?

A2: Divisibility is the property of a number that allows it to be divided by another number without leaving a remainder. For example, 6 is divisible by 2 because 6 ÷ 2 = 3.

Q3: How do I determine if a number is divisible by 2?

A3: To determine if a number is divisible by 2, you can simply check if the number ends in 0, 2, 4, 6, or 8. If it does, then the number is divisible by 2.

Q4: How do I determine if a number is divisible by 5?

A4: To determine if a number is divisible by 5, you can simply check if the number ends in 0 or 5. If it does, then the number is divisible by 5.

Q5: What is the difference between even and odd numbers?

A5: Even numbers are numbers that can be divided by 2 without leaving a remainder. Examples of even numbers include 2, 4, 6, and 8. Odd numbers are numbers that cannot be divided by 2 without leaving a remainder. Examples of odd numbers include 1, 3, 5, and 7.

Q6: How do I determine if a number is even or odd?

A6: To determine if a number is even or odd, you can simply divide the number by 2. If the number can be divided by 2 without leaving a remainder, then it is even. If the number cannot be divided by 2 without leaving a remainder, then it is odd.

Q7: What is the greatest common divisor (GCD) of two numbers?

A7: The GCD of two numbers is the largest number that can divide both numbers without leaving a remainder. For example, the GCD of 12 and 18 is 6 because 6 is the largest number that can divide both 12 and 18 without leaving a remainder.

Q8: How do I find the GCD of two numbers?

A8: To find the GCD of two numbers, you can use the Euclidean algorithm. The Euclidean algorithm is a step-by-step process that involves dividing the larger number by the smaller number and then replacing the larger number with the remainder. You repeat this process until the remainder is 0. The last non-zero remainder is the GCD.

Q9: What is the least common multiple (LCM) of two numbers?

A9: The LCM of two numbers is the smallest number that can be divided by both numbers without leaving a remainder. For example, the LCM of 12 and 18 is 36 because 36 is the smallest number that can be divided by both 12 and 18 without leaving a remainder.

Q10: How do I find the LCM of two numbers?

A10: To find the LCM of two numbers, you can use the following steps:

  1. List the multiples of each number.
  2. Identify the smallest number that appears in both lists.
  3. The smallest number that appears in both lists is the LCM.

Conclusion

In this article, we have answered some of the most frequently asked questions related to mathematics and divisibility. We hope that this article has provided valuable insights and knowledge to our readers.

References

Discussion

We would like to hear from you. Do you have any questions or comments about this article? Please feel free to share your thoughts and opinions in the discussion section below.

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