Learn how to find the GCF of 12 and 20 using and division methods. Calculation and result explained in detail.
Understanding GCF (Greatest Common Factor) of 12 and 20
Definition of GCF
The Greatest Common Factor (GCF) is the largest positive integer that divides evenly into two or more numbers. In other words, it is the largest number that is a factor of both numbers. The GCF is commonly used in mathematics to simplify fractions, find common multiples, and solve various types of problems.
Factors of 12 and 20
To find the GCF of 12 and 20, we first need to determine the factors of each number. Factors are numbers that divide evenly into a given number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of are 1, 2, 4, 5, 10, and .
Finding the GCF using Prime Factorization
One method to find the GCF of 12 and 20 is through . Prime factorization involves breaking down each number into its prime factors, which are the prime numbers that multiply together to give the original number.
To find the of , we can start by dividing it by the smallest prime number, 2. The result is 6. We continue dividing 6 by 2 until we can no longer divide evenly. The of 12 is 2 x 2 x 3.
Similarly, the prime factorization of 20 is 2 x 2 x 5.
To find the GCF, we look for the common prime factors between the two numbers. In this case, both 12 and 20 have two 2’s as common factors. Therefore, the GCF of and 20 is 2 x 2, which equals 4.
Finding the GCF using Division Method
Another method to find the GCF is through the . This method involves repeatedly dividing the larger number by the smaller number and finding the remainder. We continue this process until the remainder becomes zero. The GCF is then the last non-zero remainder obtained.
Let’s use the to find the GCF of 12 and 20. We divide 20 by 12, which gives us a quotient of 1 and a remainder of 8. We then divide by 8, resulting in a quotient of 1 and a remainder of 4. Finally, we divide 8 by 4, which gives us a quotient of 2 and a remainder of 0. Since the remainder is now zero, the GCF is the last non-zero remainder, which is 4.
GCF of 12 and 20: Calculation and Result
To summarize, the GCF of 12 and 20 can be found using either the method or the . Using , we found that the GCF is 4, as both numbers have two 2’s as common factors. Using the , we also obtained a GCF of 4, as the remainder became zero after several divisions. Therefore, the GCF of 12 and 20 is 4.
