# Greatest Common Factor Calculator

Greatest common factor (GCF) calculator. Is also known as greateset common divisor (GCD).

## GCF calculator

 First number: Second number: Greatest common factor (gcf): Least common multiple (lcm):

## GCF example

Find GCF for numbers 8 and 12:

The divisors of 8 are:

8 = 2×2×2

The divisors of 12 are:

12 = 2×2×3

So the common divisors of 8 and 12 are:

gcf = 2×2 = 4

So 8/12 fraction, can be reduced to 2/3:

8 / 12 = (8/4) / (12/4) = 2 / 3

Here we discuss list of online math calculators that help us for doing calculation easily.

### Greatest Common Factor

The GCF calculator evaluates the Greatest Common Factor between two to six different numbers. The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder. For example, for the set of numbers 18, 30 and 42 the GCF = 6.

What is GCF?

The Greatest Common Factor definition is the largest integer factor that is present between a set of numbers. It is also known as the Greatest Common Divisor, Greatest Common Denominator (GCD), Highest Common Factor (HCF), or Highest Common Divisor (HCD). This is important in certain applications of mathematics such as simplifying polynomials where often it's essential to pull out common factors. Next, we need to know how to find the GCF.

How to Find the Greatest Common Factor

There are various methods which help you to find GCF. Some of them are child's play, while others are more complex. It's worth knowing all of them so you can decide which you prefer:

Using the list of factors,

Prime factorization of numbers,

Euclidean algorithm,

Binary algorithm (Stein's algorithm),

Using multiple properties of GCF (including Least Common Multiple, LCM).

The good news is that you can estimate the GCD with simple math operations, without roots or logarithms! For most cases they are just subtraction, multiplication, or division.

Prime Factorization Method

There 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.

EX: GCF(16, 88, 104)

16 = 2 × 2 × 2 × 2

88 = 2 × 2 × 2 × 11

104 = 2 × 2 × 2 × 13

GCF(16, 88, 104) = 2 × 2 × 2 = 8

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 Algorithm

Another 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

GCF(a, b) = GCF(a-b, b), when a > b

GCF(a, b) = GCF(a, b-a), when b > a

In practice:

1. Given two positive integers, a and b, where a is larger than b, subtract the smaller number b from the larger number a, to arrive at the result c.

2. Continue subtracting b from a until the result c is smaller than b.

3. Use b as the new large number, and subtract the final result c, repeating the same process as in Step 2 until the remainder is 0.

4. Once the remainder is 0, the GCF is the remainder from the step preceding the zero result.

EX: GCF(268442, 178296)

268442 - 178296 = 90146

178296 - 90146 = 88150

90146 - 88150 = 1996

88150 - 1996 × 44 = 326

1996 - 326 × 6 = 40

326 - 40 × 8 = 6

6 - 4 = 2

4 - 2 × 2 = 0

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.