How to Find GCF of 2180/780, 7618/9478?

GCF of 2180/780, 7618/9478

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 2180/780, 7618/9478 i.e 2/3696420 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2180/780, 7618/9478.

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 2180/780,7618/9478?

Given fractions are 2180/780,7618/9478

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 2180/780,7618/9478, numerators are 2180,7618

Denominators are 780,9478

The GCF of 2180,7618 is 2 .

LCM of 780,9478 is 3696420.

The greatest common factor of 2180/780,7618/9478 = [GCF of 2180,7618]/[LCM of 780,9478]= 2/3696420

Therefore, the GCF of 2180/780,7618/9478 is 2/3696420.

Greatest Common Factor of 2180,7618

To find the highest common factor of 2180,7618, we have to find the factors of both numbers and list the highest common factor.

The factors of 2180 are 1, 2, 4, 5, 10, 20, 109, 218, 436, 545, 1090, 2180

The factors of 7618 are 1, 2, 13, 26, 293, 586, 3809, 7618

The HCF of 2180,7618 is 2.

Lets's calculate GCF of 2180,7618

Greatest Common Factor (GCF) of 2180,7618 By Common Division

2	2180, 7618
	1090, 3809

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

Greatest Common Factor of 2180,7618 By Matching Biggest Common Factor Method

Now, list down the factors of 2180

1,2,4,5,10,20,109,218,436,545,1090,2180

Now, list down the factors of 7618

1,2,13,26,293,586,3809,7618

Greatest Common Factor

We found the factors 2180,7618 . The biggest common factor number is the GCF number.
So the greatest common factor 2180,7618 is 2.

Lets's calculate LCM of 780,9478

Lowest Common Multiple of 780,9478 using Common Division

2	780, 9478
	390, 4739

∴ So the LCM of the given numbers is 2 x 390 x 4739 = 3696420

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3696420

Therefore, the GCF of Fractions 2180/780,7618/9478 is 2/3696420

Least Common Multiple of 780,9478 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 780,9478 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(780,9478) = 2

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

GCF(780,9478) x common factors =2 x 1 = 2

LCM(780,9478) = ( 780 × 9478 ) / 2

LCM(780,9478) = 7392840 / 2

LCM(780,9478) = 3696420

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FAQs on GCF of Fractions of 2180/780, 7618/9478

1. What is the HCF of 2180,7618?

The HCF of 2180,7618 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 2180/780, 7618/9478?

Answer: GCF of Numerators as per given numbers 2180/780, 7618/9478 is

GCF of Numerators i.e. for 2180,7618 is 2

LCM of denominators i.e. for 780,9478 is 3696420.

Thus, GCF of Fractions is 2/3696420.Finally, GCF of Fractions for 2180/780, 7618/9478 is 2/3696420.