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Here are some samples of Greatest Common Factor of Numbers calculations.
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Apart from the procedures on Greatest Common Factor Concept, you will also find some useful & handy Greatest Common Factor (GCF) Calculators via direct links. Access them online whenever you need within a few taps you'll just attain the accurate results for your easy to complex GCF problems. The list of free online GCF Tools are as follow:
Okay, Let's get into this Greatest Common Factor Tutorial and become a great solver in the GCF concept. Now, we'll start learning with the Basics of GCF like Greatest Common Factor definitions, Other names of GCF, and Finding GCF of Numbers with numerous methods.
In mathematics, a factor is a number or algebraic expression that divides another expression and leaves no remainder behind. In different words, if multiplying a set of whole numbers delivers us a product, then the set of numbers we are multiplying are the factors of the product because they are its exact divisor.
Additionally, Factors common in two or more numbers are called common factors.
Therefore, the Greatest common factor is nothing but the largest of all the common factors in a set of numbers.
The "Greatest Common Factor" is represented as "GCF", and is also called
the Greatest Common Divisor (GCD), or
the Highest Common Factor (HCF).
As we clearly know that the division by zero is indefinite, so zero can not be a factor of any natural number.
Therefore, the Greatest common factor(GCF) or Highest common factor(HCF) of zero is undefined.
Method 1: Listing all the factors to find the GCF
This method for finding the Greatest Common Factor is the easiest method when you have to deal with smaller numbers. To reveal the GCF of a set of numbers,
Method 2: Using prime factorization to find the GCF
This method works best for large numbers as making a list of all the factors can be time-consuming in larger numbers.
To find the GCF of a set of numbers using prime factorization:
Find the GCF of 9, 20, and 25. by listing the factors.
The Factors of 9 are 1, 3, and 9
The Factors of 20 are 2, 4, 5, 10, 20 and 1.
The Factors of 25 are 1, 5 and 25
Here, in this case, the only factor that comes out in all three number lists is 1, so 1 is the GCF of 9, 20, and 25.
Evaluate the Greatest Common Factor of 168, 252, and 288 by the prime factorization method.
The given numbers are 168, 252, and 288.
Firstly, do the prime factorization of the given numbers.
168 = 23 × 3 × 7
252 = 22 × 32 × 7
288 = 25 × 32
The GCF of these sets of numbers will be the product of the smallest power of each common prime factor of the three numbers. Therefore, the Greatest Common Factor or GCF of 168, 252, and 288 = 22 × 3 = 12.
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The calculation for the greatest common factor begins with listing out the prime factors of the selected numbers and then multiplying them to get the GCF.
You try factoring by grouping when you want to factor the polynomials without GCF.
First list all the factors of 12,
Now listing the factors of 16,
Hence the greatest common factor is 4.
7 is the greatest common factor of 21 and 28.