## GCF of Fractions Calculator

Created By : Bhagya
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Enter two or more fractions separated by "commas"

GCF of:

Here are some samples of GCF of Fractions calculations.

### What are Fractions?

In mathematical terms, a fraction is used to denote a portion or component of a whole thing. It symbolizes the proportionate equal parts of the whole. The upper part of the fraction is known as the numerator & lower part is denoted as the denominator.

### What are Factors and Common Factors?

In mathematical terms, suppose we take the number ‘x’. So, any number which divides the number ‘x’ fully without any remainder is said to be the factor of number ‘x’. Suppose we write down the factors of one or more numbers, then factors of these numbers which are the same in each factorization are said to be the common factors of the given set of numbers.

### Find the Greatest Common Factors For Given Fractions Easily

Here are the steps to find the GCF of given fractions:

1. Here, we will consider the numerator & denominator of a fraction separately.
2. Write down the prime factors of all the numbers in the numerator separately.
3. Check the list of prime factors of all numbers in numerators & Write down the common prime factors from the factorization of numerators.
4. Multiply all the common prime factors to get the GCF of all numbers in the numerator.
5. Now, write down the multiples of all the numbers in the denominator separately.
6. Check the list of multiples of all numbers in the denominator & write down a common multiple from all the multiples of the denominators.
7. Now, the common multiple is the LCM of all the numbers in the denominator.
8. To find the GCF of a fraction, divide the GCF of numerator numbers by the LCM of the denominator.

### How to Take Out HCF of Fractions Solved Example

Example:

Find the HCF of 4/3, 6/5 & 8/5.

Solution:

Here, the given fractions are 4/3, 6/5 & 8/5

Now we will first consider the numbers in the numerator i.e. 4, 6 & 8.

Now, prime factors of these numbers are:

4 = 2 × 2

6 = 2 × 3

8 = 2 × 2 × 2

From the factorization of numerators of above fractions, common factor is 2.

So, the GCF (4, 6, 8) = 2

Now we will consider the numbers in denominator i.e. 3, 5 & 5.

Now, we will write the multiples of these numbers:

Multiples of 3 = 3, 6, 9, 12, 15, 18 & so on

Multiples of 5 = 5, 10, 15, 20 & so on

Here, the least common multiple of the denominator is 15.

i.e. LCM (3, 5, 5) = 15

Now, the GCF of fractions is the division of the GCF of numerator numbers by the LCM of the denominator.

Now, GCF (4/3, 6/5, 8/5) = 2/15

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### FAQs with Steps on HCF of Fractions Calculator

• What does GCF mean in fractions?

In Fractions GCF is the largest common factor that is shared by all the numbers present. Hence, it is known as Greatest Common Factor.

• What is the HCF fraction method?

The HCF fraction method can be simply stated by a formula,

HCF of fractions = HCF of numerators/LCM of the denominators.

• What are the 3 steps to simplify fractions?

It becomes easier to simply the fractions by finding the factors for numerators and denominators, determining the HCF of them and finally performing division of the numerator and denominator by the calculated HCF.

• What are the 3 types of the fraction?

The 3 types of fractions are categorized as mixed fractions, proper fractions and improper fractions.