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First of all let us think about what a factor is. In other words, any two numbers that multiply to give a product are both factors of the product.
You will also note that 1 is a factor of all integers. So how can we find the greatest common factor? There are a number of different ways to do this, but we are going to show you two of the easiest ones: listing all the factors method prime factorization method.
This is probably the simplest way to find the gcf of any set of numbers. The only problem with this method is that it is sometimes easy to miss factors out. Example 1 Find the greatest common factor of 24 and We list the factors of both numbers: Factors of 1, 2, 3, 4, 6, 8, 12, 24 Factors of 1, 2, 4, 8, 16, 32 The common factors of 24 and 32 are: 1, 2, 4, and 8. The Greatest Common Factor is 8. Example 2 Find the greatest common factor of 60 and We list the factors of both numbers: Factors of 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 Factors of 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 The common factors of 60 and 48 are: 1, 2, 3, 4, 6, and The Greatest Common Factor is Example 3 Find the greatest common factor of 35 and We list the factors of both numbers: Factors of 1, 5, 7, 35 Factors of 1, 2, 11, 22 The only common factor of 35 and 22 is 1.
Example 4 Find the greatest common factor of 39 and We list the factors of both numbers: Factors of 1, 3, 13, 39 Factors of 1, 13 this number is prime The common factors of 39 and 13 are 1 and A factor is a smaller number that can divide evenly into that number. The greatest common factor, then, can be found when you list out the factors of each number and then find the greatest one that is in common in between the two.
Let's take a quick example: finding the greatest common factor between 9 and Let's start by factoring. Factoring is the process of finding the factors of a number.
Which is the largest number in common between the two lists? We can see that 3 is both a factor of 9 and It is the largest factor they have in common, so we can name 3 as the GCF or greatest common factor. A multiple is a larger number the number can be divided into without leaving a remainder.
For example, the multiples of 5 are 5, 10, 15, 20, 25, and so on. We will find the prime factorization of each of these numbers. The GCF of these three numbers will be the product of the prime factors of all three numbers. Among the given numbers, is the largest, and is the smallest. We will divide the larger number by the smaller number.
Next, we will make the remainder as the divisor and the last divisor as the dividend and divide again. We will repeat this process until the remainder is 0. A common factor of two or more numbers is a factor that is common to both of the given numbers.
For example, the common factors of 45 and 25 are 1 and 5. The greatest number among all the common factors of two or more numbers is called the greatest common factor or GCF. For any two numbers, the GCF is the largest number that divides the two given numbers. GCF can be calculated by using the basic arithmetic operations in mathematics i.
To find the greatest common factor of two or more natural numbers , there are 3 methods that can be used. Namely, listing out of the common factors, prime factorization, and division method.
Each method requires division and multiplication to obtain the GCF. For example, the GCF of 14 and 35 is 7. By using the listing common factors method, the factors of 14 are 1, 2, 7, 14 and the factors of 35 are 1, 5, 7, The two common factors are 1 and 7. A prime number has only two factors 1 and itself.
Hence, two prime numbers cannot have any common factor other than 1. Therefore, the greatest common factor of two prime numbers is 1. For example, the greatest common factor of 5 and 7 is 1.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and The factors of 15 are 1, 3, 5, and The common factors of 24 and 15 are 1 and 3.
Hence, the GCF of 24 and 15 is 3. The factors of 20 are 1, 2, 4, 5, 10, and The common factors of 15 and 20 are 1 and 5. Thus, the GCF of 15 and 20 is 5. GCF of two or more numbers can be obtained by using the prime factorization method that is done only in a few steps.
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