Explanation And Solution For Gcf Of 28 And 42

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Introduction

In the world of mathematics, the concept of greatest common factor (GCF) is essential. GCF is the highest number that can divide two or more numbers without leaving a remainder. Finding the GCF of two numbers is crucial in simplifying fractions and solving certain math problems. In this article, we will discuss the GCF of 28 and 42.

Calculation

To find the GCF of 28 and 42, we need to list down all the factors of each number. The factors of 28 are 1, 2, 4, 7, 14, and 28. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. The common factors of both numbers are 1, 2, 7, and 14. The highest common factor between 28 and 42 is 14.

Explanation

The factors of a number are any numbers that can divide the original number without leaving a remainder. For example, the factors of 28 are 1, 2, 4, 7, 14, and 28. One is always a factor of any number. Two is a factor because 28 divided by 2 equals 14, which is a whole number. Four is a factor because 28 divided by 4 equals 7. Seven is a factor because 28 divided by 7 equals 4. Lastly, 14 is a factor because 28 divided by 14 equals 2. Similarly, the factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. One is always a factor of any number. Two is a factor because 42 divided by 2 equals 21, which is a whole number. Three is a factor because 42 divided by 3 equals 14. Six is a factor because 42 divided by 6 equals 7. Seven is a factor because 42 divided by 7 equals 6. Fourteen is a factor because 42 divided by 14 equals 3. Lastly, 21 is a factor because 42 divided by 21 equals 2.

Solution

To find the GCF of 28 and 42, we need to list down all the factors of each number. The factors of 28 are 1, 2, 4, 7, 14, and 28. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. We can easily identify the common factors of both numbers, which are 1, 2, 7, and 14. However, we need to find the highest common factor, which is 14. Therefore, the GCF of 28 and 42 is 14.

Importance of GCF

The concept of GCF is important in mathematics because it helps to simplify fractions. When reducing a fraction, we can divide both the numerator and denominator by their GCF to get the simplest form of the fraction. For example, if we want to simplify the fraction 28/42, we can divide both the numerator and denominator by their GCF, which is 14. Therefore, 28/42 simplifies to 2/3.

Conclusion

In conclusion, the GCF of 28 and 42 is 14. The factors of both numbers are essential in finding their GCF. The concept of GCF is important in mathematics as it simplifies fractions, making them easier to work with.