How to Find GCF of 47/274, 78/691, 749/676?

GCF of 47/274, 78/691, 749/676

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 47/274, 78/691, 749/676 i.e 1/63994892 easily. The following is the detailed procedure to determine the greatest common factor of fractions 47/274, 78/691, 749/676.

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 47/274,78/691,749/676?

Given fractions are 47/274,78/691,749/676

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 47/274,78/691,749/676, numerators are 47,78,749

Denominators are 274,691,676

The GCF of 47,78,749 is 1 .

LCM of 274,691,676 is 63994892.

The greatest common factor of 47/274,78/691,749/676 = [GCF of 47,78,749]/[LCM of 274,691,676]= 1/63994892

Therefore, the GCF of 47/274,78/691,749/676 is 1/63994892.

Greatest Common Factor of 47,78,749

To find the highest common factor of 47,78,749, we have to find the factors of both numbers and list the highest common factor.

The factors of 47 are 1, 47

The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78

The factors of 749 are 1, 7, 107, 749

The HCF of 47,78,749 is 1.

Lets's calculate GCF of 47,78,749

Greatest Common Factor (GCF) of 47,78,749 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 47,78,749 By Matching Biggest Common Factor Method

Now, list down the factors of 47

1,47

Now, list down the factors of 78

1,2,3,6,13,26,39,78

Now, list down the factors of 749

1,7,107,749

Greatest Common Factor

We found the factors 47,78,749 . The biggest common factor number is the GCF number.
So the greatest common factor 47,78,749 is 1.

Lets's calculate LCM of 274,691,676

Lowest Common Multiple of 274,691,676 using Common Division

2	274, 691, 676
	137, 691, 338

∴ So the LCM of the given numbers is 2 x 137 x 691 x 338 = 63994892

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/63994892

Therefore, the GCF of Fractions 47/274,78/691,749/676 is 1/63994892

Least Common Multiple of 274,691,676 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 274,691,676 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(274,691,676) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(274,691,676) x common factors =1 x 2 = 2

LCM(274,691,676) = ( 274 × 691 × 676 ) / 2

LCM(274,691,676) = 127989784 / 2

LCM(274,691,676) = 63994892

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 47/274, 78/691, 749/676

1. What is the HCF of 47,78,749?

The HCF of 47,78,749 is 1

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 47/274, 78/691, 749/676?

Answer: GCF of Numerators as per given numbers 47/274, 78/691, 749/676 is

GCF of Numerators i.e. for 47,78,749 is 1

LCM of denominators i.e. for 274,691,676 is 63994892.

Thus, GCF of Fractions is 1/63994892.Finally, GCF of Fractions for 47/274, 78/691, 749/676 is 1/63994892.