The Greatest Common Factor Of 21 And 28

GCF of 21 and 28 How to Find GCF of 21, 28? from en.asriportal.com

What is a Greatest Common Factor (GCF)?

A Greatest Common Factor, also known as GCF, is the largest number that can divide two or more numbers without leaving a remainder. In other words, it is the biggest factor that two or more numbers have in common.

How to Find the GCF of 21 and 28?

To find the GCF of 21 and 28, we need to list down all the factors of both numbers. Factors are the numbers that can be multiplied to get a specific number. For example, the factors of 21 are 1, 3, 7, and 21, while the factors of 28 are 1, 2, 4, 7, 14, and 28.

Prime Factorization Method

One of the easiest ways to find GCF is by using the Prime Factorization method. We need to find the prime factors of both numbers and then multiply the common factors. To do this, we need to break down 21 and 28 into their prime factors. The prime factors of 21 are 3 and 7, while the prime factors of 28 are 2, 2, 7. We can see that both numbers have a common factor of 7. Therefore, the GCF of 21 and 28 is 7.

Division Method

Another way to find the GCF of 21 and 28 is by using the Division method. We need to divide the larger number by the smaller number and find the remainder. Then, we divide the smaller number by the remainder and find the new remainder. We keep doing this until we get a remainder of zero. Let's use this method to find the GCF of 21 and 28. We divide 28 by 21, and the remainder is 7. Then, we divide 21 by 7, and the remainder is zero. Therefore, the GCF of 21 and 28 is 7.

Why is Finding GCF Important?

Finding the GCF is essential in simplifying fractions. We can divide both the numerator and denominator of a fraction by their GCF to get the simplest form of the fraction. For example, if we need to simplify the fraction 21/28, we can divide both numbers by their GCF, which is 7. Thus, 21/28 simplifies to 3/4.

In Conclusion

Finding the GCF of 21 and 28 is essential in simplifying fractions or solving problems related to factors. There are different methods to find the GCF, such as Prime Factorization and Division. However, both methods will give the same result, which is 7.