How to Find GCF of 108/638, 768/854?

GCF of 108/638, 768/854

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 108/638, 768/854 i.e 12/272426 easily. The following is the detailed procedure to determine the greatest common factor of fractions 108/638, 768/854.

Enter two or more fractions separated by "commas"

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

What is the GCF of 108/638,768/854?

Given fractions are 108/638,768/854

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 108/638,768/854, numerators are 108,768

Denominators are 638,854

The GCF of 108,768 is 12 .

LCM of 638,854 is 272426.

The greatest common factor of 108/638,768/854 = [GCF of 108,768]/[LCM of 638,854]= 12/272426

Therefore, the GCF of 108/638,768/854 is 12/272426.

Greatest Common Factor of 108,768

To find the highest common factor of 108,768, we have to find the factors of both numbers and list the highest common factor.

The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108

The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768

The HCF of 108,768 is 12.

Lets's calculate GCF of 108,768

Greatest Common Factor (GCF) of 108,768 By Common Division

2	108, 768
2	54, 384
3	27, 192
	9, 64

∴ So the GCF of the given numbers is 2 x 2 x 3 = 12

Greatest Common Factor of 108,768 By Matching Biggest Common Factor Method

Now, list down the factors of 108

1,2,3,4,6,9,12,18,27,36,54,108

Now, list down the factors of 768

1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768

Greatest Common Factor

We found the factors 108,768 . The biggest common factor number is the GCF number.
So the greatest common factor 108,768 is 12.

Lets's calculate LCM of 638,854

Lowest Common Multiple of 638,854 using Common Division

2	638, 854
	319, 427

∴ So the LCM of the given numbers is 2 x 319 x 427 = 272426

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/272426

Therefore, the GCF of Fractions 108/638,768/854 is 12/272426

Least Common Multiple of 638,854 with GCF Formula

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

We need to calculate greatest common factor of 638,854 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(638,854) = 2

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

GCF(638,854) x common factors =2 x 1 = 2

LCM(638,854) = ( 638 × 854 ) / 2

LCM(638,854) = 544852 / 2

LCM(638,854) = 272426

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FAQs on GCF of Fractions of 108/638, 768/854

1. What is the HCF of 108,768?

The HCF of 108,768 is 12

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 108/638, 768/854?

Answer: GCF of Numerators as per given numbers 108/638, 768/854 is

GCF of Numerators i.e. for 108,768 is 12

LCM of denominators i.e. for 638,854 is 272426.

Thus, GCF of Fractions is 12/272426.Finally, GCF of Fractions for 108/638, 768/854 is 12/272426.