The answer depends on what it is of two or more numbers that you wish to find.
greatest common factor
Example: What are the common prime factors of 120 and 252?Find the prime factorization of each number by breaking it down into the lowest possible numbers that can be multiplied together to make the original number.120 = 2x60 = 2x2x30 = 2x2x2x15 = 2x2x2x3x5252 = 2x126 = 2x2x63 = 2x2x3x21 = 2x2x3x3x7Notice that there are 2 2's and a 3 in each factorization: the common prime factors are 2, 2, and 3.
Because both numbers are prime numbers, the only common factor they have is 1. Therefore, the greatest common factor is 1. Another way to determine the greatest common factor is to find all the factors of the numbers and compare them. The factors of 5 are 1 and 5. The factors of 23 are 1 and 23. The only common factor is 1. Therefore, the greatest common factor is 1, which means the numbers are relatively prime. The greatest common factor can also be calculated by identifying the common prime factors and multiplying them together. The prime factor of 5 is 5. The prime factor of 23 is 23. There are no prime factors in common, so the numbers are relatively prime, which means the greatest common factor is 1.
You do not. To have a greatest common factor, you need two or more numbers. A common factor is a factor that two or more number have in common. However, the prime factorization of all the numbers will help you find the greatest common factor. The greatest common factor will be the prime factors they have in common multiplied together. Example: The prime factors of 45 are 3, 3, and 5. The prime factors of 60 are 2, 2, 3, and 5. The common prime factors are 3 and 5, so the greatest common factor is 3 x 5 = 15.
One way to determine the greatest common factor is to find all the factors of the numbers and compare them. The factors of 65 are 1, 5, 13, and 65. The factors of 213 are 1, 3, 71, and 213. The only common factor is 1. Therefore, the greatest common factor is 1, which means the numbers are relatively prime. The greatest common factor can also be calculated by identifying the common prime factors and multiplying them together. The prime factors of 65 are 5 and 13. The prime factors of 213 are 3 and 71. There are no prime factors in common, so the numbers are relatively prime, which means the greatest common factor is 1.
You do not necessarily need the common prime factors when finding the greatest common factor, but with large numbers or numbers for which you cannot easily determine all the factors, using prime factorization to determine the greatest common factor is the easiest method. The greatest common factor can then be determined by multiplying the common prime factors together. For example, when trying to find the greatest common factor of 2144 and 5672, finding all their possible factors to compare could be difficult. So, it is easier to find their prime factors, determine the prime factors they have in common, and then multiply the common prime factors to get the greatest common factor. For descriptions and examples of finding the greatest common factor, see the "Related Questions" links below.
Example: What are the common prime factors of 120 and 252?Find the prime factorization of each number by breaking it down into the lowest possible numbers that can be multiplied together to make the original number.120 = 2x60 = 2x2x30 = 2x2x2x15 = 2x2x2x3x5252 = 2x126 = 2x2x63 = 2x2x3x21 = 2x2x3x3x7Notice that there are 2 2's and a 3 in each factorization: the common prime factors are 2, 2, and 3.
Calculate their prime factors.
By finding their prime factors
do the prime factorization of the 3 numbers. list the prime factors of all the 3 numbers. circle the factors that are common to the 3. multiply them. that number is the HCF
To find the greatest common factor (GCF), first find the prime factorization of the two numbers. The GCF is the product of all of the prime factors the two numbers have in common. If two numbers have no common factors, the GCF is 1. (Since all numbers are divisible by 1.) Example: Find the GCF of 60 and 24. Prime factors of 60: 2, 2, 3, 5 Prime factors of 24: 2, 2, 2, 3 Common factors: 2, 2, 3 GCF: 2x2x3=12 Example: Find the GCF of 17 and 21. Prime factors of 17: 17 Prime factors of 21: 3, 7 Common factors: None (1). GCF: 1
To find the greatest common factor (GCF), first find the prime factorization of the two numbers. The GCF is the product of all of the prime factors the two numbers have in common. If two numbers have no common factors, the GCF is 1. (Since all numbers are divisible by 1.) Prime factors of 545: 5, 109 Prime factors of 1024: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 They have in common: Nothing. The GCF is 1.
If they have no prime factors in common, their GCF is 1.
To simplify a fraction using prime numbers, find the prime factors of both the numerator and denominator. Then, divide the numerator and denominator by their common prime factors. Repeat this process until there are no common prime factors left. The resulting fraction will be simplified to its simplest form.
All composite numbers have prime factors and these are used to find the highest common factor of 2 or more numbers and they are also used in finding the lowest common multiple of 2 or more numbers. Composite numbers have 2 or more factors while prime numbers have only 2 factors which are themselves and one
To find the greatest common factor (GCF), first find the prime factorization of the two numbers. The GCF is the product of all of the prime factors the two numbers have in common. Prime factors of 28: 2, 2, 7 Prime factors of 68: 2, 2, 17 They have in common: 2, 2. 2x2=4 The GCF is 4.
If you take all the common prime factors between numbers and multiply them it will give you the gcf.
By finding their common prime numbers.