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What is Greatest Common Factor?

Factorization organizes the features in the form of a common factor. In which all the factors detached from a single numeric value. The factorization further leads the classification for common factors as Greatest Common Factor.

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Greatest Common Factor definition

The greatest common factor (GCF) of two non-zero integers is the largest positive integer which divides the numbers without a remainder. It is known as the greatest common denominator, highest common factor (HCF) or greatest common divisor (GCD).

GCF formula

We can calculate the Greatest factor or GCF by two different formulations of gcf formula

First Play

When two or more numbers in a factor matched, the largest factor is greatest common factor.

Second Play

If we represent two numbers (16 & 24) as products of their prime factors.

  • 16 = 2 x 2 x 2 x 2
  • 24 = 2 x 2 x 2 x 3

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We repeatedly get the three 2’s like a common value. Then the multiple of these repeated integers provides us the GCF.

  • GCF = 2 x 2 x 2 = 8

Since factorization is not efficient, this is sensible for small numbers. The item expression shows that the best common divisor is found by following property. It divides equally and GCD is a divisor.

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How to find GCF?

It is a fun to estimate the GCF for any particular set of data when there’s proper guidance for its solution. Below, the easiest tracks reflect the resolution for simple to complex questions.

The steps to find greatest common factor are:

Step #1: Find the prime factorization.

Factors of 12: 1, 2, 3, 4, 6, 12.

Factors of 16: 1, 2, 4, 8, 16.

Step #2: Excluded out the common factors.

Common factors = 1, 2, 4

Step #3: Picked the largest value out of the common factor.

“4” is the greatest common factor.

This way briefly highlights the route for expressive and accurate answers with negligible input of headache.

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How to find GCF and LCM fast?

To calculate LCM, one must be familiar with its cleared implementation. More often you build fractions with discrete denominators to find the common denominator.

In arithmetic, the smallest common multiple of two non-zero integers a and b is the smallest positive integer. It is also a multiple of these two numbers.

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What are the steps to find LCM?

The LCM can be calculated by following these easy steps:

Step #1: Take out GCF for any two values (like 30 & 14), which is 2.

Step #2: Divide 2 with either of the values, say 30/2 = 15.

Step #3: Multiply 15 with the second remaining value to get direct LCM.

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GCF Finder

By retaining the above-mentioned details in a summarized manner, GCF is easy to find. Dealing with multi-dimensional or decimal numeric, the GCF has no specific margins. There is only a method throughout the heterogeneous conditions could solve it.

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Mathematical relation for LCM and GCF

If we’ve calculated the lcm out of them both, we can easily find GCF by using the following relation.

“Product of two values = GCF of the numbers x LCM of the numbers.”

Case #1: If HCF is known and LCM is unknown:

$$\text{LCM}\;=\;\frac{\text{Product of numbers}}{\text{GCF of numbers}}$$

Case #2: If HCF is unknown and LCM is known:

$$\text{GCF}\;=\;\frac{\text{Product of numbers}}{\text{LCM of numbers}}$$

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What is the GCF of 12 and 4?

The greatest common factor of 12 and 4 can be calculated by making prime factorization. Picking matched pairs from both values and then marked out the greatest factor from them.

Practical Derivation

Prime factorization,

  • 12 = 1, 2, 3, 4, 6, 12
  • 4 = 1, 2, 4

1, 2 and 4 are common factors and 4 is the Highest Common factor or GCF of 12 & 4.

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What is GCF Calculator?

With the advancement of the scientific approach, calculators play an important role. Calculators manage time and provide quick and accurate calculations.

GCF calculator is pivotal in the circle of factorization and its extensions. By using GCF calculator of calculatored, the integers on-screen directly revert to the exact answer. This is also known as GCF Finder in technical terms and oriented to the way of calculations.

How to use GCF Calculator?

GCF calculator is simple and easy to use. The features of this tool provide wise and direct answer. There’s no specific limit of numbers in the GCF calculator.

You just need to enter your number into gcf calculator and click "Calculate" button. Our online tool will provide you greatest common factor and steps of factorization.

We hope our greatest common factor calculator and this article helped you in learning and practice. Our portal also offer matrix calculator and limit calculator to learn the calculations of other math subjects.


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