How to Find GCF of 8239/214, 6703/4560?

GCF of 8239/214, 6703/4560

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 8239/214, 6703/4560 i.e 1/487920 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8239/214, 6703/4560.

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 8239/214,6703/4560?

Given fractions are 8239/214,6703/4560

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 8239/214,6703/4560, numerators are 8239,6703

Denominators are 214,4560

The GCF of 8239,6703 is 1 .

LCM of 214,4560 is 487920.

The greatest common factor of 8239/214,6703/4560 = [GCF of 8239,6703]/[LCM of 214,4560]= 1/487920

Therefore, the GCF of 8239/214,6703/4560 is 1/487920.

Greatest Common Factor of 8239,6703

To find the highest common factor of 8239,6703, we have to find the factors of both numbers and list the highest common factor.

The factors of 8239 are 1, 7, 11, 77, 107, 749, 1177, 8239

The factors of 6703 are 1, 6703

The HCF of 8239,6703 is 1.

Lets's calculate GCF of 8239,6703

Greatest Common Factor (GCF) of 8239,6703 By Common Division

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

Greatest Common Factor of 8239,6703 By Matching Biggest Common Factor Method

Now, list down the factors of 8239

1,7,11,77,107,749,1177,8239

Now, list down the factors of 6703

1,6703

Greatest Common Factor

We found the factors 8239,6703 . The biggest common factor number is the GCF number.
So the greatest common factor 8239,6703 is 1.

Lets's calculate LCM of 214,4560

Lowest Common Multiple of 214,4560 using Common Division

2	214, 4560
	107, 2280

∴ So the LCM of the given numbers is 2 x 107 x 2280 = 487920

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/487920

Therefore, the GCF of Fractions 8239/214,6703/4560 is 1/487920

Least Common Multiple of 214,4560 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 214,4560 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(214,4560) = 2

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

GCF(214,4560) x common factors =2 x 1 = 2

LCM(214,4560) = ( 214 × 4560 ) / 2

LCM(214,4560) = 975840 / 2

LCM(214,4560) = 487920

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FAQs on GCF of Fractions of 8239/214, 6703/4560

1. What is the HCF of 8239,6703?

The HCF of 8239,6703 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 8239/214, 6703/4560?

Answer: GCF of Numerators as per given numbers 8239/214, 6703/4560 is

GCF of Numerators i.e. for 8239,6703 is 1

LCM of denominators i.e. for 214,4560 is 487920.

Thus, GCF of Fractions is 1/487920.Finally, GCF of Fractions for 8239/214, 6703/4560 is 1/487920.