GCF Calculator is a free math tool that shows the big common number among two given numbers. However, Mathcalculator online **GFC calculator** accomplishes the calculation faster and easier & provides a GCF within a second.

In other words, The GCF calculator tool determines the Greatest Common Factor between the two to six various numbers. Stay with this article to know **“What is the Greatest Common Factor of given numbers?”**. Also, study the different GCF finder techniques along with prime factorization. Then, to make this calculation short and faster, use our GCF calculator.

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## What is the Greatest Common Factor (GCF)?

The GCF or Greatest Common Factor answer is **the largest integer factor present between a set of numbers**. It is more familiar as the Greatest Common Divisor, Greatest Common Denominator (GCD), Highest Common Factor (HCF), or Highest Common Divisor (HCD).

This is necessary for many applications of mathematics, such as ‘Simplifying polynomials’ where typically it’s essential to get off general factors. So now, we should understand how to attain GCF?

Let’s proceed with the step-by-step process to know how to find the GCF.

**How to find the Greatest Common Factor?**

Various methods help you in finding GCF. Many are so simple, and others are adamant. It’s a judgment to know all of them so that you can determine which is more helpful:

- Using the list of factors,
- Prime factorization of numbers,
- Euclidean algorithm,
- Binary algorithm,
- Using multiple properties of GCF, including LCM.

You can also get the GCD with easy math calculations, without roots or logarithms!

**GCF Finder- list of Common elements:**

The primary method to evaluate the Greatest Common Divisor is to catch all of the common factors from the given numbers. Factors are techniques to guess the numbers that multiplied with each other and produced a final number. Commonly, both positive and negative numbers, e.g. **2*3** are the same as **(-2)*(-3)**, all equal to **6**. So, to complete the calculation, we always consider a positive number. Furthermore, only integers are disturbed.

Let’s find out the GCD of numbers 72 and 40.

**Ex:**

- Factor of 72 are: 1,2,3,4,6,8,9,12,18,24,36,72
- Factor of 40: 1,2,4,5,8,10,20,40,
- Common factors: 1,2,4,8

Finally, the **Greatest Common Divisor is 8**, the big value from the common factors.

**Let’s continue with another example:**

**Question:** What is the Greatest Common Factor of 33264 & 35640?

**Ans: **Let’s start finding the factor of both numbers:

**Factor of 33264:**1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 16, 18, 21, 22, 24, 27, 28, 33, 36, 42, 44, 48, 54, 56, 63, 66, 72, 77, 84, 88, 99, 108, 112, 126, 132, 144, 154, 168, 176, 189, 198, 216, 231, 252, 264, 297, 308, 336, 378, 396, 432, 462, 504, 528, 594, 616, 693, 756, 792, 924, 1008, 1188, 1232, 1386, 1512, 1584, 1848, 2079, 2376, 2772, 3024, 3696, 4158, 4752, 5544, 8316, 11088, 16632, 33264**Factors of 35640:**1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 18, 20, 22, 24, 27, 30, 33, 36, 40, 44, 45, 54, 55, 60, 66, 72, 81, 88, 90, 99, 108, 110, 120, 132, 135, 162, 165, 180, 198, 216, 220, 264, 270, 297, 324, 330, 360, 396, 405, 440, 495, 540, 594, 648, 660, 792, 810, 891, 990, 1080, 1188, 1320, 1485, 1620, 1782, 1980, 2376, 2970, 3240, 3564, 3960, 4455, 5940, 7128, 8910, 11880, 17820, 35640,

**Now pick the common factors from the list:** 1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 27, 33, 36, 44, 54, 66, 72, 88, 99, 108, 132, 198, 216, 264, 297, 396, 594, 792, 1188, 2376

**F****inal answer:** To check the Greatest Common Factor, select the large number from this list of final common factors. So, the final answer is: **2376**

As you see, finding the GCF from the list of numbers is not a cup of tea. It can be a mistake while you are finding the Greatest Common Factor. So, we recommend using an online HCF Calculator to make it easy and find it fastly.