The greatest common factor of two or more numbers (also called the greatest common factor or the highest common factor or the greatest common divisor) is the largest number that gives an integer as a result when both numbers are divided by it. The easiest way to calculate the GCF of two numbers is to list all the factors of those numbers and choose the ones they have in
common. The largest of those factors is the greatest common divisor. For example, let us look at the numbers 27 and 45 and calculate their GCF. The number 27 can be divided by numbers 1, 3 and 9. The number 47 is divisible by numbers 1, 3, 5, 9 and 15. The divisors they have in common are 1, 3 and 9. The largest of them is 9 and it is their greatest common divisor. It is also possible to calculate the GCF by using prime factorizations and determining how many factors the two numbers have in
common. The shared factors are then multiplied and the result is the GCF. For example, the prime factors of number 64 are 2*2*2*2*2*2 and the prime factors of number 72 are 2*2*2*3*3. The factors they have in common are 2*2*2. So, after we multiply these factors we get 8 as the result and ther greatest common factor. This method is only practical for smaller numbers, since prime factorization of large numbers takes a lot of time. Show Example: Number 12 will give an integer as a result when it is divided by numbers 1, 2, 3, 4, 6 and 12. Number 18 can be divided by 1, 2, 3, 6, 9 and 18. That means that the largest common factor
of the numbers 12 and 18 is 6, since 12 cannot be divided by 9 and 18 and still give an integer as a result. Greatest common factor exams for teachers
Greatest common factor worksheets for students
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How do you find the greatest common factor of monomials?Greatest common factors in monomials
Simply write the complete factorization of each monomial and find the common factors. The product of all the common factors will be the GCF.
How do you find the greatest monomial factor and common monomial factor?To find the greatest common factor (GCF) between monomials, take each monomial and write it's prime factorization. Then, identify the factors common to each monomial and multiply those common factors together. Bam! The GCF!
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