Which Of The Following Numbers Is A Multiple Of 6?A. 106 B. 333 C. 424 D. 882

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Introduction

In mathematics, a multiple of a number is the product of that number and an integer. In this case, we are looking for a number that is a multiple of 6. To determine which of the given options is a multiple of 6, we need to understand the properties of multiples and how to identify them.

What is a Multiple of 6?

A multiple of 6 is any number that can be expressed as the product of 6 and an integer. For example, 6 × 1 = 6, 6 × 2 = 12, 6 × 3 = 18, and so on. Any number that can be expressed in this form is a multiple of 6.

Properties of Multiples of 6

Multiples of 6 have several properties that can help us identify them. One of the key properties is that they are always divisible by 6. This means that if a number is a multiple of 6, it can be divided by 6 without leaving a remainder.

How to Identify Multiples of 6

To identify a multiple of 6, we can use the following methods:

  • Divisibility Rule: If a number is divisible by 6, it is a multiple of 6. To check if a number is divisible by 6, we can divide it by 6 and check if the remainder is 0.
  • Prime Factorization: We can also use prime factorization to identify multiples of 6. A multiple of 6 must have 2 and 3 as its prime factors.

Analyzing the Options

Now that we understand the properties of multiples of 6, let's analyze the given options:

  • Option A: 106: To determine if 106 is a multiple of 6, we can divide it by 6 and check if the remainder is 0. 106 ÷ 6 = 17.67, which means that 106 is not a multiple of 6.
  • Option B: 333: To determine if 333 is a multiple of 6, we can divide it by 6 and check if the remainder is 0. 333 ÷ 6 = 55.5, which means that 333 is not a multiple of 6.
  • Option C: 424: To determine if 424 is a multiple of 6, we can divide it by 6 and check if the remainder is 0. 424 ÷ 6 = 70.67, which means that 424 is not a multiple of 6.
  • Option D: 882: To determine if 882 is a multiple of 6, we can divide it by 6 and check if the remainder is 0. 882 ÷ 6 = 147, which means that 882 is a multiple of 6.

Conclusion

In conclusion, the correct answer is Option D: 882. This is because 882 is a multiple of 6, as it can be expressed as 6 × 147. The other options, 106, 333, and 424, are not multiples of 6.

Why is it Important to Identify Multiples of 6?

Identifying multiples of 6 is important in various mathematical operations, such as:

  • Division: When dividing a number by 6, we need to know if the number is a multiple of 6 to get the correct quotient.
  • Multiplication: When multiplying a number by 6, we need to know if the number is a multiple of 6 to get the correct product.
  • Fractions: When working with fractions, we need to know if the numerator or denominator is a multiple of 6 to simplify the fraction.

Real-World Applications of Multiples of 6

Multiples of 6 have various real-world applications, such as:

  • Time: There are 6 hours in a standard clock, and multiples of 6 are used to measure time.
  • Money: There are 6 coins in a standard US dollar, and multiples of 6 are used to calculate change.
  • Geometry: Multiples of 6 are used to calculate the area and perimeter of rectangles and squares.

Final Thoughts

Q: What is a multiple of 6?

A: A multiple of 6 is any number that can be expressed as the product of 6 and an integer. For example, 6 × 1 = 6, 6 × 2 = 12, 6 × 3 = 18, and so on.

Q: How do I identify a multiple of 6?

A: To identify a multiple of 6, you can use the following methods:

  • Divisibility Rule: If a number is divisible by 6, it is a multiple of 6. To check if a number is divisible by 6, you can divide it by 6 and check if the remainder is 0.
  • Prime Factorization: You can also use prime factorization to identify multiples of 6. A multiple of 6 must have 2 and 3 as its prime factors.

Q: What are some examples of multiples of 6?

A: Some examples of multiples of 6 include:

  • 6 × 1 = 6
  • 6 × 2 = 12
  • 6 × 3 = 18
  • 6 × 4 = 24
  • 6 × 5 = 30

Q: Can I use a calculator to find multiples of 6?

A: Yes, you can use a calculator to find multiples of 6. Simply multiply 6 by the desired integer and the result will be a multiple of 6.

Q: Are all multiples of 6 even numbers?

A: No, not all multiples of 6 are even numbers. For example, 6 × 3 = 18, which is an even number, but 6 × 5 = 30, which is also an even number. However, 6 × 1 = 6, which is an even number, and 6 × 7 = 42, which is also an even number.

Q: Can I use multiples of 6 to solve real-world problems?

A: Yes, you can use multiples of 6 to solve real-world problems. For example, if you are planning a party and you want to serve 6 guests per table, you can use multiples of 6 to determine how many tables you will need.

Q: Are multiples of 6 used in any mathematical formulas?

A: Yes, multiples of 6 are used in some mathematical formulas. For example, the formula for the area of a rectangle is A = lw, where A is the area, l is the length, and w is the width. If the length and width are both multiples of 6, the area will also be a multiple of 6.

Q: Can I use multiples of 6 to create a pattern?

A: Yes, you can use multiples of 6 to create a pattern. For example, you can create a pattern of numbers that are multiples of 6, such as 6, 12, 18, 24, 30, and so on.

Q: Are multiples of 6 used in any scientific applications?

A: Yes, multiples of 6 are used in some scientific applications. For example, in physics, the speed of light is approximately 6 × 10^8 meters per second, which is a multiple of 6.

Q: Can I use multiples of 6 to solve algebraic equations?

A: Yes, you can use multiples of 6 to solve algebraic equations. For example, if you have an equation such as 2x + 6 = 12, you can use multiples of 6 to solve for x.

Conclusion

In conclusion, multiples of 6 are an important mathematical concept that has various real-world applications. By understanding the properties of multiples of 6, you can identify them easily and apply them in various mathematical operations.