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GCF Calculator

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Introduction to GCF Calculator

Factorization organizes the features in the form of a common factor. In which all the factors are detached from a single numeric value. The factorization further leads to classifying common factors as the greatest common factors.

Calculatored has designed this greatest common factor calculator, which accurately finds the common factor within seconds. You only have to give the number in this online tool and click on the calculate button. The common factor will be on your screen within seconds.

What is Greatest Common Factor?

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

The formula used in GCF finder

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

First Method

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

Second Method

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

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

  • GCF = 2 x 2 x 2 = 8

Related: To calculate factors only, use the factor algebra calculator for free.

The GCF calculator with solution uses both methods in its algorithm. The tool analyzes the numbers given in the functionality bar and approaches for the quickest and best method to give you the greatest common factor. The results are always correct and accurate.

Since factorization is not efficient, this is sensible for small numbers. The item expression shows that the following property finds the best common divisor. Our tool divides equally, and GCD would be a divisor.

How does the GCF Algebra Calculator find GCF?

It is fun to estimate the GCF for our GCF calculator with steps. GCF of any particular set of data is solved with its solution. Below, the steps are used in this GCF finder. You can also learn how to solve them.

The steps used to factor out the greatest common factor calculator are:

Step #1: Finding the prime factorization.

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

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

Step #2: Excluding the common factors.

Common factors = 1, 2, 4

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

“4” is the greatest common factor.

This way, briefly and accurate answers with negligible input are given to you on the screen.

Benefits of Greatest Common Factor Calculator Algebra

By retaining the details mentioned above summarised, 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 that could solve it. With the advancement of the scientific approach, calculators play an important role. Calculators manage time and provide quick and accurate calculations.

To easily find gcf calculator algebra, which is pivotal in the circle of factorization and its extensions, you only have to search the tool's name in calculatored. Using the GCF calculator with variables of calculatored, the integers on-screen directly revert to the exact answer. It is also known as GCF finder in technical terms and is oriented to the way of calculations.

How to use Greatest Common Factor 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 with variables.

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

Click here to learn about the calculations of roots of equations with quadratic function calculator.


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 marking 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.

How to find GCF and LCM fast?

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

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

What are the steps to finding LCM?

The LCM is 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.

Mathematical relation for LCM and GCF

We can easily find GCF by using the following relation if we've calculated the lcm out of them both.

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

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

LCM = Product of numbers/GCF of numbers

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

GCF = Product of numbers/LCM of numbers

We hope our greatest common factor calculator and this article helped you learn and practice. Our portal also offers a symmetric matrix solver.

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Shaun Murphy

Last updated: September 09, 2020

I'm graduated in biomedical and electrical engineering. Specialization in sports and medical topics but will gladly tackle everything you throw at him. He is a sailor, hiker, and motorcyclist in his free time.

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