Understanding Factors and Multiples

Oct 13, 2025 by pinkandtrash.com 110 views

Introduction

In mathematics, factors and multiples are two fundamental concepts that are often used to describe the relationships between numbers. A factor of a number is an integer that can be multiplied by another integer to produce the original number, while a multiple of a number is the result of multiplying the number by an integer. In this article, we will explore the concept of a number that is both a factor and a multiple of 90, and we will examine the properties of such a number.

Understanding Factors and Multiples

To begin with, let's define what factors and multiples are. A factor of a number is an integer that can be multiplied by another integer to produce the original number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. On the other hand, a multiple of a number is the result of multiplying the number by an integer. For example, the multiples of 12 are 12, 24, 36, 48, and so on.

The Relationship Between Factors and Multiples

Now, let's examine the relationship between factors and multiples. A factor of a number is always a multiple of the number, but a multiple of a number is not always a factor. For example, 3 is a factor of 12, but 12 is a multiple of 3. However, 12 is not a factor of 12, but it is a multiple of 12.

Finding a Number that is Both a Factor and a Multiple of 90

To find a number that is both a factor and a multiple of 90, we need to look for a number that can be multiplied by another number to produce 90, and also can be divided by another number to produce 90. In other words, we need to find a number that is both a divisor and a product of 90.

The Number 90 is its own Factor and Multiple

One number that is both a factor and a multiple of 90 is 90 itself. This may seem obvious, but it is worth noting that 90 is its own factor and multiple. When we multiply 90 by 1, we get 90, which is a multiple of 90. Similarly, when we divide 90 by 1, we get 90, which is a factor of 90.

Other Numbers that are Both Factors and Multiples of 90

In addition to 90, there are other numbers that are both factors and multiples of 90. For example, 1 is a factor of 90, and when we multiply 1 by 90, we get 90, which is a multiple of 90. Similarly, 10 is a factor of 90, and when we multiply 10 by 9, we get 90, which is a multiple of 90.

Conclusion

In conclusion, one number that is both a factor and a multiple of 90 is 90 itself. However, there are other numbers that are also both factors and multiples of 90, such as 1 and 10. Understanding the relationship between factors and multiples is an important concept in mathematics, and it can be used to solve a wide range of problems.

Factors and Multiples of 90

Here are the factors and multiples of 90:

Factors of 90

Multiples of 90

90
180
270
360
450
540
630
720
810
900
990
1080

Examples of Numbers that are Both Factors and Multiples of 90

Here are some examples of numbers that are both factors and multiples of 90:

1: 1 is a factor of 90, and when we multiply 1 by 90, we get 90, which is a multiple of 90.
10: 10 is a factor of 90, and when we multiply 10 by 9, we get 90, which is a multiple of 90.
90: 90 is a factor of 90, and when we multiply 90 by 1, we get 90, which is a multiple of 90.

Applications of Factors and Multiples

Understanding factors and multiples has many practical applications in mathematics and real-life situations. For example, in finance, understanding the factors and multiples of a stock's price can help investors make informed decisions about buying or selling the stock. In engineering, understanding the factors and multiples of a machine's design can help engineers optimize the machine's performance.

Conclusion

Introduction

In our previous article, we explored the concept of a number that is both a factor and a multiple of 90. We examined the properties of such a number and found that 90 itself is a number that is both a factor and a multiple of 90. However, we also found that there are other numbers that are also both factors and multiples of 90, such as 1 and 10. In this article, we will answer some frequently asked questions about factors and multiples of 90.

Q&A

Q: What is the difference between a factor and a multiple?

A: A factor of a number is an integer that can be multiplied by another integer to produce the original number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. On the other hand, a multiple of a number is the result of multiplying the number by an integer. For example, the multiples of 12 are 12, 24, 36, 48, and so on.

Q: How do I find the factors and multiples of a number?

A: To find the factors of a number, you can start by listing the numbers that divide the number evenly. For example, to find the factors of 12, you can start by listing the numbers that divide 12 evenly: 1, 2, 3, 4, 6, and 12. To find the multiples of a number, you can multiply the number by different integers. For example, to find the multiples of 12, you can multiply 12 by different integers: 12, 24, 36, 48, and so on.

Q: What is the relationship between factors and multiples?

A: A factor of a number is always a multiple of the number, but a multiple of a number is not always a factor. For example, 3 is a factor of 12, but 12 is a multiple of 3. However, 12 is not a factor of 12, but it is a multiple of 12.

Q: Can a number be both a factor and a multiple of itself?

A: Yes, a number can be both a factor and a multiple of itself. For example, 90 is a factor of 90, and when we multiply 90 by 1, we get 90, which is a multiple of 90.

Q: How do I use factors and multiples in real-life situations?

A: Understanding factors and multiples has many practical applications in mathematics and real-life situations. For example, in finance, understanding the factors and multiples of a stock's price can help investors make informed decisions about buying or selling the stock. In engineering, understanding the factors and multiples of a machine's design can help engineers optimize the machine's performance.

Q: What are some examples of numbers that are both factors and multiples of 90?

A: Some examples of numbers that are both factors and multiples of 90 are 1, 10, and 90 itself. For example, 1 is a factor of 90, and when we multiply 1 by 90, we get 90, which is a multiple of 90. Similarly, 10 is a factor of 90, and when we multiply 10 by 9, we get 90, which is a multiple of 90.

Q: Can I use a calculator to find the factors and multiples of a number?

A: Yes, you can use a calculator to find the factors and multiples of a number. However, it's also important to understand the underlying math concepts and to be able to do the calculations by hand.

Q: How do I find the greatest common factor (GCF) and the least common multiple (LCM) of two numbers?

A: To find the GCF of two numbers, you can list the factors of each number and find the greatest factor that they have in common. To find the LCM of two numbers, you can list the multiples of each number and find the smallest multiple that they have in common.

Conclusion

In conclusion, understanding factors and multiples is an important concept in mathematics, and it has many practical applications in real-life situations. By understanding the relationship between factors and multiples, you can solve a wide range of problems and make informed decisions in finance, engineering, and other fields.

Factors and Multiples of 90

Here are the factors and multiples of 90:

Factors of 90

Multiples of 90

90
180
270
360
450
540
630
720
810
900
990
1080

Examples of Numbers that are Both Factors and Multiples of 90

Here are some examples of numbers that are both factors and multiples of 90:

1: 1 is a factor of 90, and when we multiply 1 by 90, we get 90, which is a multiple of 90.
10: 10 is a factor of 90, and when we multiply 10 by 9, we get 90, which is a multiple of 90.
90: 90 is a factor of 90, and when we multiply 90 by 1, we get 90, which is a multiple of 90.