Please provide numbers separated by a comma "," and click the "Calculate" button to find the GCF. Show
What is the Greatest Common Factor (GCF)?In mathematics, the greatest common factor (GCF), also known as the greatest common divisor, of two (or more) non-zero integers a and b, is the largest positive integer by which both integers can be divided. It is commonly denoted as GCF(a, b). For example, GCF(32, 256) = 32. Prime Factorization MethodThere are multiple ways to find the greatest common factor of given integers. One of these involves computing the prime factorizations of each integer, determining which factors they have in common, and multiplying these factors to find the GCD. Refer to the example below.
Prime factorization is only efficient for smaller integer values. Larger values would make the prime factorization of each and the determination of the common factors, far more tedious. Euclidean AlgorithmAnother method used to determine the GCF involves using the Euclidean algorithm. This method is a far more efficient method than the use of prime factorization. The Euclidean algorithm uses a division algorithm combined with the observation that the GCD of two integers can also divide their difference. The algorithm is as follows: GCF(a, a) = a In practice:
From the example above, it can be seen that GCF(268442, 178296) = 2. If more integers were present, the same process would be performed to find the GCF of the subsequent integer and the GCF of the previous two integers. Referring to the previous example, if instead the desired value were GCF(268442, 178296, 66888), after having found that GCF(268442, 178296) is 2, the next step would be to calculate GCF(66888, 2). In this particular case, it is clear that the GCF would also be 2, yielding the result of GCF(268442, 178296, 66888) = 2. Example: x^2+5x+4 Example (Click to try)x^2+5x+4 How to factor expressionsIf you are factoring a quadratic like x^2+5x+4 you want to find two numbers that
Since 1 and 4
add up to 5 and multiply together to get 4, we can factor it like: Current calculator limitations
Factoring Expressions Video Lesson How To Factor x^2+5x+4 [0:58] Need more problem types? Try MathPapa Algebra Calculator
How do you factor an expression using GCF?To factor out the GCF in an expression like the one above, first find the GCF of all of the expression's terms. Next, divide each term from the original expression (3x3+27x2+9x ) by the GCF (3x), then write it in the parenthesis.
How do you factor expressions?To find the GCF of an expression, follow these steps:. Write each term as the. prime factorization. of the coefficient or constant, listing any variables separately. For example, write. x. y. as. x. y. , and write. x. as. x. x. .. Identify the factors that all of the terms have in common.. Multiply those common factors.. What is the GCF for 30 and 54?The GCF of 30 and 54 is 6.
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