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GCF of 770/76, 278/6756

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 770/76, 278/6756 i.e 2/128364 easily. The following is the detailed procedure to determine the greatest common factor of fractions 770/76, 278/6756.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 770/76,278/6756?

Given fractions are 770/76,278/6756

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 770/76,278/6756, numerators are 770,278

Denominators are 76,6756

The GCF of 770,278 is 2 .

LCM of 76,6756 is 128364.

The greatest common factor of 770/76,278/6756 = [GCF of 770,278]/[LCM of 76,6756]= 2/128364

Therefore, the GCF of 770/76,278/6756 is 2/128364.

Greatest Common Factor of 770,278

To find the highest common factor of 770,278, we have to find the factors of both numbers and list the highest common factor.

The factors of 770 are 1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385, 770

The factors of 278 are 1, 2, 139, 278

The HCF of 770,278 is 2.

Lets's calculate GCF of 770,278

Greatest Common Factor (GCF) of 770,278 By Common Division

2 770, 278
385, 139

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

Greatest Common Factor of 770,278 By Matching Biggest Common Factor Method

Greatest Common Factor of 770,278 By Matching Biggest Common Factor Method

Now, list down the factors of 770

:

1,2,5,7,10,11,14,22,35,55,70,77,110,154,385,770

Now, list down the factors of 278

:

1,2,139,278

Greatest Common Factor

We found the factors 770,278 . The biggest common factor number is the GCF number.
So the greatest common factor 770,278 is 2.

Lets's calculate LCM of 76,6756

Lowest Common Multiple of 76,6756 using Common Division

2 76, 6756
2 38, 3378
19, 1689

∴ So the LCM of the given numbers is 2 x 2 x 19 x 1689 = 128364

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/128364

Therefore, the GCF of Fractions 770/76,278/6756 is 2/128364

Least Common Multiple of 76,6756 with GCF Formula

Least Common Multiple of 76,6756 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 76,6756 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(76,6756) = 4

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

GCF(76,6756) x common factors =4 x 1 = 4

LCM(76,6756) = ( 76 × 6756 ) / 4

LCM(76,6756) = 513456 / 4

LCM(76,6756) = 128364


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FAQs on GCF of Fractions of 770/76, 278/6756

1. What is the HCF of 770,278?

The HCF of 770,278 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 770/76, 278/6756?

Answer: GCF of Numerators as per given numbers 770/76, 278/6756 is

GCF of Numerators i.e. for 770,278 is 2

LCM of denominators i.e. for 76,6756 is 128364.

Thus, GCF of Fractions is 2/128364.Finally, GCF of Fractions for 770/76, 278/6756 is 2/128364.