How to Find GCF of 1792/861, 9974/6814?

GCF of 1792/861, 9974/6814

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 1792/861, 9974/6814 i.e 2/5866854 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1792/861, 9974/6814.

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 1792/861,9974/6814?

Given fractions are 1792/861,9974/6814

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 1792/861,9974/6814, numerators are 1792,9974

Denominators are 861,6814

The GCF of 1792,9974 is 2 .

LCM of 861,6814 is 5866854.

The greatest common factor of 1792/861,9974/6814 = [GCF of 1792,9974]/[LCM of 861,6814]= 2/5866854

Therefore, the GCF of 1792/861,9974/6814 is 2/5866854.

Greatest Common Factor of 1792,9974

To find the highest common factor of 1792,9974, we have to find the factors of both numbers and list the highest common factor.

The factors of 1792 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 896, 1792

The factors of 9974 are 1, 2, 4987, 9974

The HCF of 1792,9974 is 2.

Lets's calculate GCF of 1792,9974

Greatest Common Factor (GCF) of 1792,9974 By Common Division

2	1792, 9974
	896, 4987

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

Greatest Common Factor of 1792,9974 By Matching Biggest Common Factor Method

Now, list down the factors of 1792

1,2,4,7,8,14,16,28,32,56,64,112,128,224,256,448,896,1792

Now, list down the factors of 9974

1,2,4987,9974

Greatest Common Factor

We found the factors 1792,9974 . The biggest common factor number is the GCF number.
So the greatest common factor 1792,9974 is 2.

Lets's calculate LCM of 861,6814

Lowest Common Multiple of 861,6814 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 5866854

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/5866854

Therefore, the GCF of Fractions 1792/861,9974/6814 is 2/5866854

Least Common Multiple of 861,6814 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 861,6814 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(861,6814) = 1

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

GCF(861,6814) x common factors =1 x 1 = 1

LCM(861,6814) = ( 861 × 6814 ) / 1

LCM(861,6814) = 5866854 / 1

LCM(861,6814) = 5866854

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FAQs on GCF of Fractions of 1792/861, 9974/6814

1. What is the HCF of 1792,9974?

The HCF of 1792,9974 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 1792/861, 9974/6814?

Answer: GCF of Numerators as per given numbers 1792/861, 9974/6814 is

GCF of Numerators i.e. for 1792,9974 is 2

LCM of denominators i.e. for 861,6814 is 5866854.

Thus, GCF of Fractions is 2/5866854.Finally, GCF of Fractions for 1792/861, 9974/6814 is 2/5866854.