• Home
• >
• Knowledge Base
• >
• Factors of 42 – Definition With Examples

Factors of 42 – Definition With Examples

Welcome, brilliant minds! Here at Brighterly, we’re passionate about making learning math fun and engaging for children. We believe that every child has a mathematician within them waiting to be unleashed. Today, we’ll explore an intriguing aspect of mathematics: the factors of 42! This simple yet important concept forms the cornerstone of many mathematical principles. Ready to learn and have fun? Let’s dive right in!

What Are Factors?

Factors are a fundamental concept in mathematics. They are numbers that can evenly divide another number without leaving a remainder. In other words, a factor is a number that can be multiplied with another number to yield the original number. For example, for the number 6, its factors are 1, 2, 3, and 6, because these numbers can be multiplied together in pairs to produce 6 (16, 23).

Definition of Factors of a Number

In mathematics, the factors of a number are whole numbers that can be divided evenly into that number. Think of it like breaking down a number into its smallest building blocks. These blocks are its factors, and they are incredibly useful in many areas of mathematics, from simplifying fractions to solving complex equations.

Definition of Factors of 42

Now, let’s talk about the factors of 42. These are all the numbers that can divide 42 evenly. In this case, the factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. You can check this by dividing 42 by any of these numbers, and you will see that there’s no remainder.

Properties of Factors

Every number has its own unique set of factors, and these factors have some interesting properties. For one, every number’s factors include 1 and the number itself. Also, the factors of a number are always less than or equal to that number. For example, the factors of 10 are 1, 2, 5, and 10.

Properties of Factors of 42

Like every number, 42 has its own factors and their properties. The factors of 42, as we mentioned earlier, are 1, 2, 3, 6, 7, 14, 21, and 42. The sum of these factors is 96, and their product gives back the original number when arranged appropriately.

Difference Between Factors and Multiples

It’s important to understand the difference between factors and multiples. While factors are numbers that can be divided evenly into a number, multiples are numbers that can be evenly divided by that number. For example, multiples of 7 are numbers like 14, 21, 28, and so on, while its factors are just 1 and 7.

How to Determine the Factors of a Number

One common method to determine the factors of a number is to start dividing the number by other numbers. Start from 1 and go up to the number itself. If the division leaves no remainder, then the divisor is a factor.

Method of Finding Factors of 42

To find the factors of 42, you can follow the method above. Start from 1, and check whether each number divides 42 without leaving a remainder. When you do this, you will find that the factors are 1, 2, 3, 6, 7, 14, 21, and 42.

Examples of Finding Factors of Other Numbers

Just like we found the factors of 42, you can find the factors of any number. For example, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. And so on.

Practice Problems on Finding Factors of 42

Let’s get to the exciting part – practice problems! Practicing is the best way to reinforce your understanding and get better at finding factors. Ready? Here are some problems for you:

1. Find the factors of 36

   To find the factors of 36, start dividing 36 from 1 up to the number itself. When you do this, you will find that 36 can be evenly divided by 1, 2, 3, 4, 6, 9, 12, 18, and 36. So, these are the factors of 36.

2. Find the factors of 48

   Now, let’s find the factors of 48. Start by dividing 48 by numbers from 1 to 48. You will find that the numbers 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48 can evenly divide 48. Hence, these are the factors of 48.

3. Find the factors of 60

   Finally, let’s find the factors of 60. Divide 60 by numbers from 1 to 60. The numbers that can divide 60 without leaving a remainder are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. These are the factors of 60.

Conclusion

Congratulations on completing another enlightening lesson at Brighterly! Today, we learned about the factors of 42, explored the unique properties of factors, and differentiated between factors and multiples. We hope that this deeper understanding of factors will light the way as you continue your journey through the fascinating world of mathematics.

Remember, the path to mastering math is paved with practice, and we encourage you to solve the practice problems we’ve provided. Don’t hesitate to revisit the lesson and review any concepts that may still seem challenging. Learning at your own pace is what Brighterly is all about.

Frequently Asked Questions on Factors of 42

What is a prime factor?

A prime factor of a number is a factor that is a prime number. Prime numbers are numbers that have only two factors: 1 and themselves. For example, the prime factors of 42 are 2, 3, and 7.

What is the greatest common factor (GCF)?

The greatest common factor (GCF) is the largest factor that two or more numbers have in common. For example, the GCF of 42 and 56 is 14.

Why do we need to find factors?

Finding factors is essential in many areas of mathematics. They are especially useful in simplifying fractions, finding the least common multiple (LCM), and solving problems involving division and fractions.

Is 42 a prime number or a composite number?

42 is a composite number because it has more than two factors. Remember, prime numbers only have two factors: 1 and the number itself.