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GCF of 306/89, 172/638

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

Use our free GCF of Fractions Calculator tool to compute the GCF of 306/89, 172/638 i.e 2/56782 easily. The following is the detailed procedure to determine the greatest common factor of fractions 306/89, 172/638.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 306/89,172/638?

Given fractions are 306/89,172/638

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 306/89,172/638, numerators are 306,172

Denominators are 89,638

The GCF of 306,172 is 2 .

LCM of 89,638 is 56782.

The greatest common factor of 306/89,172/638 = [GCF of 306,172]/[LCM of 89,638]= 2/56782

Therefore, the GCF of 306/89,172/638 is 2/56782.

Greatest Common Factor of 306,172

To find the highest common factor of 306,172, we have to find the factors of both numbers and list the highest common factor.

The factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306

The factors of 172 are 1, 2, 4, 43, 86, 172

The HCF of 306,172 is 2.

Lets's calculate GCF of 306,172

Greatest Common Factor (GCF) of 306,172 By Common Division

2 306, 172
153, 86

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 306,172 By Matching Biggest Common Factor Method

Greatest Common Factor of 306,172 By Matching Biggest Common Factor Method

Now, list down the factors of 306

:

1,2,3,6,9,17,18,34,51,102,153,306

Now, list down the factors of 172

:

1,2,4,43,86,172

Greatest Common Factor

We found the factors 306,172 . The biggest common factor number is the GCF number.
So the greatest common factor 306,172 is 2.

Lets's calculate LCM of 89,638

Lowest Common Multiple of 89,638 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 56782

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/56782

Therefore, the GCF of Fractions 306/89,172/638 is 2/56782

Least Common Multiple of 89,638 with GCF Formula

Least Common Multiple of 89,638 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 89,638 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(89,638) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(89,638) x common factors =1 x 1 = 1

LCM(89,638) = ( 89 × 638 ) / 1

LCM(89,638) = 56782 / 1

LCM(89,638) = 56782


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FAQs on GCF of Fractions of 306/89, 172/638

1. What is the HCF of 306,172?

The HCF of 306,172 is 2

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 306/89, 172/638?

Answer: GCF of Numerators as per given numbers 306/89, 172/638 is

GCF of Numerators i.e. for 306,172 is 2

LCM of denominators i.e. for 89,638 is 56782.

Thus, GCF of Fractions is 2/56782.Finally, GCF of Fractions for 306/89, 172/638 is 2/56782.