How to Find GCF of 754/31, 770/3738?

GCF of 754/31, 770/3738

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 754/31, 770/3738 i.e 2/115878 easily. The following is the detailed procedure to determine the greatest common factor of fractions 754/31, 770/3738.

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 754/31,770/3738?

Given fractions are 754/31,770/3738

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 754/31,770/3738, numerators are 754,770

Denominators are 31,3738

The GCF of 754,770 is 2 .

LCM of 31,3738 is 115878.

The greatest common factor of 754/31,770/3738 = [GCF of 754,770]/[LCM of 31,3738]= 2/115878

Therefore, the GCF of 754/31,770/3738 is 2/115878.

Greatest Common Factor of 754,770

To find the highest common factor of 754,770, we have to find the factors of both numbers and list the highest common factor.

The factors of 754 are 1, 2, 13, 26, 29, 58, 377, 754

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

The HCF of 754,770 is 2.

Lets's calculate GCF of 754,770

Greatest Common Factor (GCF) of 754,770 By Common Division

2	754, 770
	377, 385

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

Greatest Common Factor of 754,770 By Matching Biggest Common Factor Method

Now, list down the factors of 754

1,2,13,26,29,58,377,754

Now, list down the factors of 770

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

Greatest Common Factor

We found the factors 754,770 . The biggest common factor number is the GCF number.
So the greatest common factor 754,770 is 2.

Lets's calculate LCM of 31,3738

Lowest Common Multiple of 31,3738 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 115878

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/115878

Therefore, the GCF of Fractions 754/31,770/3738 is 2/115878

Least Common Multiple of 31,3738 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 31,3738 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,3738) = 1

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

GCF(31,3738) x common factors =1 x 1 = 1

LCM(31,3738) = ( 31 × 3738 ) / 1

LCM(31,3738) = 115878 / 1

LCM(31,3738) = 115878

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FAQs on GCF of Fractions of 754/31, 770/3738

1. What is the HCF of 754,770?

The HCF of 754,770 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 754/31, 770/3738?

Answer: GCF of Numerators as per given numbers 754/31, 770/3738 is

GCF of Numerators i.e. for 754,770 is 2

LCM of denominators i.e. for 31,3738 is 115878.

Thus, GCF of Fractions is 2/115878.Finally, GCF of Fractions for 754/31, 770/3738 is 2/115878.