How to Find GCF of 2797/360, 7814/6876?

GCF of 2797/360, 7814/6876

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 2797/360, 7814/6876 i.e 1/68760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2797/360, 7814/6876.

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 2797/360,7814/6876?

Given fractions are 2797/360,7814/6876

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 2797/360,7814/6876, numerators are 2797,7814

Denominators are 360,6876

The GCF of 2797,7814 is 1 .

LCM of 360,6876 is 68760.

The greatest common factor of 2797/360,7814/6876 = [GCF of 2797,7814]/[LCM of 360,6876]= 1/68760

Therefore, the GCF of 2797/360,7814/6876 is 1/68760.

Greatest Common Factor of 2797,7814

To find the highest common factor of 2797,7814, we have to find the factors of both numbers and list the highest common factor.

The factors of 2797 are 1, 2797

The factors of 7814 are 1, 2, 3907, 7814

The HCF of 2797,7814 is 1.

Lets's calculate GCF of 2797,7814

Greatest Common Factor (GCF) of 2797,7814 By Common Division

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

Greatest Common Factor of 2797,7814 By Matching Biggest Common Factor Method

Now, list down the factors of 2797

1,2797

Now, list down the factors of 7814

1,2,3907,7814

Greatest Common Factor

We found the factors 2797,7814 . The biggest common factor number is the GCF number.
So the greatest common factor 2797,7814 is 1.

Lets's calculate LCM of 360,6876

Lowest Common Multiple of 360,6876 using Common Division

2	360, 6876
2	180, 3438
3	90, 1719
3	30, 573
	10, 191

∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 10 x 191 = 68760

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/68760

Therefore, the GCF of Fractions 2797/360,7814/6876 is 1/68760

Least Common Multiple of 360,6876 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 360,6876 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(360,6876) = 36

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

GCF(360,6876) x common factors =36 x 1 = 36

LCM(360,6876) = ( 360 × 6876 ) / 36

LCM(360,6876) = 2475360 / 36

LCM(360,6876) = 68760

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FAQs on GCF of Fractions of 2797/360, 7814/6876

1. What is the HCF of 2797,7814?

The HCF of 2797,7814 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 2797/360, 7814/6876?

Answer: GCF of Numerators as per given numbers 2797/360, 7814/6876 is

GCF of Numerators i.e. for 2797,7814 is 1

LCM of denominators i.e. for 360,6876 is 68760.

Thus, GCF of Fractions is 1/68760.Finally, GCF of Fractions for 2797/360, 7814/6876 is 1/68760.