How to Find GCF of 3080/780, 7139/676?

GCF of 3080/780, 7139/676

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 3080/780, 7139/676 i.e 11/10140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3080/780, 7139/676.

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 3080/780,7139/676?

Given fractions are 3080/780,7139/676

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 3080/780,7139/676, numerators are 3080,7139

Denominators are 780,676

The GCF of 3080,7139 is 11 .

LCM of 780,676 is 10140.

The greatest common factor of 3080/780,7139/676 = [GCF of 3080,7139]/[LCM of 780,676]= 11/10140

Therefore, the GCF of 3080/780,7139/676 is 11/10140.

Greatest Common Factor of 3080,7139

To find the highest common factor of 3080,7139, we have to find the factors of both numbers and list the highest common factor.

The factors of 3080 are 1, 2, 4, 5, 7, 8, 10, 11, 14, 20, 22, 28, 35, 40, 44, 55, 56, 70, 77, 88, 110, 140, 154, 220, 280, 308, 385, 440, 616, 770, 1540, 3080

The factors of 7139 are 1, 11, 59, 121, 649, 7139

The HCF of 3080,7139 is 11.

Lets's calculate GCF of 3080,7139

Greatest Common Factor (GCF) of 3080,7139 By Common Division

11	3080, 7139
	280, 649

∴ So the GCF of the given numbers is 11 = 11

Greatest Common Factor of 3080,7139 By Matching Biggest Common Factor Method

Now, list down the factors of 3080

1,2,4,5,7,8,10,11,14,20,22,28,35,40,44,55,56,70,77,88,110,140,154,220,280,308,385,440,616,770,1540,3080

Now, list down the factors of 7139

1,11,59,121,649,7139

Greatest Common Factor

We found the factors 3080,7139 . The biggest common factor number is the GCF number.
So the greatest common factor 3080,7139 is 11.

Lets's calculate LCM of 780,676

Lowest Common Multiple of 780,676 using Common Division

2	780, 676
2	390, 338
13	195, 169
	15, 13

∴ So the LCM of the given numbers is 2 x 2 x 13 x 15 x 13 = 10140

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/10140

Therefore, the GCF of Fractions 3080/780,7139/676 is 11/10140

Least Common Multiple of 780,676 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 780,676 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(780,676) = 52

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

GCF(780,676) x common factors =52 x 1 = 52

LCM(780,676) = ( 780 × 676 ) / 52

LCM(780,676) = 527280 / 52

LCM(780,676) = 10140

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FAQs on GCF of Fractions of 3080/780, 7139/676

1. What is the HCF of 3080,7139?

The HCF of 3080,7139 is 11

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 3080/780, 7139/676?

Answer: GCF of Numerators as per given numbers 3080/780, 7139/676 is

GCF of Numerators i.e. for 3080,7139 is 11

LCM of denominators i.e. for 780,676 is 10140.

Thus, GCF of Fractions is 11/10140.Finally, GCF of Fractions for 3080/780, 7139/676 is 11/10140.