How to Find GCF of 55/686, 78/704, 499/861?

GCF of 55/686, 78/704, 499/861

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 55/686, 78/704, 499/861 i.e 1/29701056 easily. The following is the detailed procedure to determine the greatest common factor of fractions 55/686, 78/704, 499/861.

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 55/686,78/704,499/861?

Given fractions are 55/686,78/704,499/861

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 55/686,78/704,499/861, numerators are 55,78,499

Denominators are 686,704,861

The GCF of 55,78,499 is 1 .

LCM of 686,704,861 is 29701056.

The greatest common factor of 55/686,78/704,499/861 = [GCF of 55,78,499]/[LCM of 686,704,861]= 1/29701056

Therefore, the GCF of 55/686,78/704,499/861 is 1/29701056.

Greatest Common Factor of 55,78,499

To find the highest common factor of 55,78,499, we have to find the factors of both numbers and list the highest common factor.

The factors of 55 are 1, 5, 11, 55

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

The factors of 499 are 1, 499

The HCF of 55,78,499 is 1.

Lets's calculate GCF of 55,78,499

Greatest Common Factor (GCF) of 55,78,499 By Common Division

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

Greatest Common Factor of 55,78,499 By Matching Biggest Common Factor Method

Now, list down the factors of 55

1,5,11,55

Now, list down the factors of 78

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

Now, list down the factors of 499

1,499

Greatest Common Factor

We found the factors 55,78,499 . The biggest common factor number is the GCF number.
So the greatest common factor 55,78,499 is 1.

Lets's calculate LCM of 686,704,861

Lowest Common Multiple of 686,704,861 using Common Division

2	686, 704, 861
7	343, 352, 861
	49, 352, 123

∴ So the LCM of the given numbers is 2 x 7 x 49 x 352 x 123 = 29701056

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/29701056

Therefore, the GCF of Fractions 55/686,78/704,499/861 is 1/29701056

Least Common Multiple of 686,704,861 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 686,704,861 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(686,704,861) = 1

common factors(in case of two or more numbers have common factors) = 14

GCF(686,704,861) x common factors =1 x 14 = 14

LCM(686,704,861) = ( 686 × 704 × 861 ) / 14

LCM(686,704,861) = 415814784 / 14

LCM(686,704,861) = 29701056

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 55/686, 78/704, 499/861

1. What is the HCF of 55,78,499?

The HCF of 55,78,499 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 55/686, 78/704, 499/861?

Answer: GCF of Numerators as per given numbers 55/686, 78/704, 499/861 is

GCF of Numerators i.e. for 55,78,499 is 1

LCM of denominators i.e. for 686,704,861 is 29701056.

Thus, GCF of Fractions is 1/29701056.Finally, GCF of Fractions for 55/686, 78/704, 499/861 is 1/29701056.