GCF Calculator

Use our online Greatest Common Factor (GCF) calculator to find GCF of two or more numbers along with step by step working (Solution). Also learn how to calculate GCF using factoring and other methods. Easy to use free SMK's online GCF calculator that finds out the greatest common factor of any numbers. It is also called the highest common factor (HCF) or greatest common divisor (GCD) or greatest common factor (GCF).

Explore other calculators or unit converters or try out our GCF Calculator and learn more about GCF .

Solution:

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GCF Calculator Details

What is GCF?

Greatest Common Factor (GCF) of 2 or more numbers is the largest factor that all the numbers share, which is same as the greatest positive value that divides the numbers.

When factors of 2 or more numbers are found, there can be some factors that are common for all the numbers. The highest of these factors would be called the Greatest or Highest Common Factor.

GCF or Greatest Common Factor is also known as Greatest Common Divisor (GCD) as the remainder of the given set of numbers, after division with this greatest common factor, would be 0

How do you calculate the GCF?

Learn how can you find the greatest common factor (GCF) of two or more numbers. There are various ways to find Greatest Common Factor for given set of numbers

Calculating GCF using Factoring

For each number, list down all the factors and then find the largest number common in all the lists

For Example, Find the GCF of 330, 75, 450, 225

Factors of 330: 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, 330
Factors of 75: 1, 3, 5, 15, 25, 75
Factors of 450: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
Factors of 225: 1, 3, 5, 9, 15, 25, 45, 75, 225

Hence, GCF(330, 75, 450, 225) = 15

Calculating GCF using Prime Factorization

For each number, calculate the prime factorization
Find out the common prime factors for all the numbers
Multiply these factors to find GCF

For Example, Find the GCF of 330, 75, 450, 225

The prime factorization of 330 = 2 x 3 x 5 x 11
The prime factorization of 75 = 3 x 5 x 5
The prime factorization of 450 = 2 x 3 x 3 x 5 x 5
The prime factorization of 225 = 3 x 3 x 5 x 5

GCF(330, 75, 450, 225) = 3 x 5 = 15

Calculating GCF using Euclid’s Algorithm

For a given numbers, Take the largest number ‘a’ and subtract the next largest number ‘b’ from it
Subtract the next largest number ‘b’ again from the result (a-b) and keep on doing that till the result becomes smaller that the second largest number ‘b’
Subtract the result from the next largest number ‘b’ and keep on doing that till result becomes 0
The number which was last subtracted from the result will be the GCF of number a,b
If there are more than 2 numbers then the same process will be repeated for GCF (a,b) and the next largest number in the set OR for the other 2 set of number and then the GCFs till we get one GCF for the given set

For Example, Find the GCF of 330, 75, 450, 225

Following Euclid’s method, let’s take the largest number 450 and next largest number 330

450-330 = 120

330-120-120 = 90

120-90 = 30

90-30-30-30=0

GCF (450,330) = 30

Considering the other two numbers 225,75

225-75-75-75 = 0

GCF(225,750) = 75

Now, considering GCF (450,330) and GCF(225,750) i.e. 30 and 75

75-30-30=15