How to Find GCF of 8274/320, 5477/6870?

GCF of 8274/320, 5477/6870

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 8274/320, 5477/6870 i.e 1/219840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8274/320, 5477/6870.

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 8274/320,5477/6870?

Given fractions are 8274/320,5477/6870

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 8274/320,5477/6870, numerators are 8274,5477

Denominators are 320,6870

The GCF of 8274,5477 is 1 .

LCM of 320,6870 is 219840.

The greatest common factor of 8274/320,5477/6870 = [GCF of 8274,5477]/[LCM of 320,6870]= 1/219840

Therefore, the GCF of 8274/320,5477/6870 is 1/219840.

Greatest Common Factor of 8274,5477

To find the highest common factor of 8274,5477, we have to find the factors of both numbers and list the highest common factor.

The factors of 8274 are 1, 2, 3, 6, 7, 14, 21, 42, 197, 394, 591, 1182, 1379, 2758, 4137, 8274

The factors of 5477 are 1, 5477

The HCF of 8274,5477 is 1.

Lets's calculate GCF of 8274,5477

Greatest Common Factor (GCF) of 8274,5477 By Common Division

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

Greatest Common Factor of 8274,5477 By Matching Biggest Common Factor Method

Now, list down the factors of 8274

1,2,3,6,7,14,21,42,197,394,591,1182,1379,2758,4137,8274

Now, list down the factors of 5477

1,5477

Greatest Common Factor

We found the factors 8274,5477 . The biggest common factor number is the GCF number.
So the greatest common factor 8274,5477 is 1.

Lets's calculate LCM of 320,6870

Lowest Common Multiple of 320,6870 using Common Division

2	320, 6870
5	160, 3435
	32, 687

∴ So the LCM of the given numbers is 2 x 5 x 32 x 687 = 219840

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/219840

Therefore, the GCF of Fractions 8274/320,5477/6870 is 1/219840

Least Common Multiple of 320,6870 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 320,6870 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(320,6870) = 10

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

GCF(320,6870) x common factors =10 x 1 = 10

LCM(320,6870) = ( 320 × 6870 ) / 10

LCM(320,6870) = 2198400 / 10

LCM(320,6870) = 219840

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 8274/320, 5477/6870

1. What is the HCF of 8274,5477?

The HCF of 8274,5477 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 8274/320, 5477/6870?

Answer: GCF of Numerators as per given numbers 8274/320, 5477/6870 is

GCF of Numerators i.e. for 8274,5477 is 1

LCM of denominators i.e. for 320,6870 is 219840.

Thus, GCF of Fractions is 1/219840.Finally, GCF of Fractions for 8274/320, 5477/6870 is 1/219840.