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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.
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.
Here are the steps to find the GCF of given fractions:
Find the HCF of 4/3, 6/5 & 8/5.
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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In Fractions GCF is the largest common factor that is shared by all the numbers present. Hence, it is known as Greatest Common Factor.
The HCF fraction method can be simply stated by a formula,
HCF of fractions = HCF of numerators/LCM of the denominators.
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.
The 3 types of fractions are categorized as mixed fractions, proper fractions and improper fractions.