How to Find GCF of 770/409, 1036/814?

GCF of 770/409, 1036/814

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 770/409, 1036/814 i.e 14/332926 easily. The following is the detailed procedure to determine the greatest common factor of fractions 770/409, 1036/814.

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 770/409,1036/814?

Given fractions are 770/409,1036/814

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 770/409,1036/814, numerators are 770,1036

Denominators are 409,814

The GCF of 770,1036 is 14 .

LCM of 409,814 is 332926.

The greatest common factor of 770/409,1036/814 = [GCF of 770,1036]/[LCM of 409,814]= 14/332926

Therefore, the GCF of 770/409,1036/814 is 14/332926.

Greatest Common Factor of 770,1036

To find the highest common factor of 770,1036, 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 1036 are 1, 2, 4, 7, 14, 28, 37, 74, 148, 259, 518, 1036

The HCF of 770,1036 is 14.

Lets's calculate GCF of 770,1036

Greatest Common Factor (GCF) of 770,1036 By Common Division

2	770, 1036
7	385, 518
	55, 74

∴ So the GCF of the given numbers is 2 x 7 = 14

Greatest Common Factor of 770,1036 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 1036

1,2,4,7,14,28,37,74,148,259,518,1036

Greatest Common Factor

We found the factors 770,1036 . The biggest common factor number is the GCF number.
So the greatest common factor 770,1036 is 14.

Lets's calculate LCM of 409,814

Lowest Common Multiple of 409,814 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 332926

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/332926

Therefore, the GCF of Fractions 770/409,1036/814 is 14/332926

Least Common Multiple of 409,814 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 409,814 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(409,814) = 1

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

GCF(409,814) x common factors =1 x 1 = 1

LCM(409,814) = ( 409 × 814 ) / 1

LCM(409,814) = 332926 / 1

LCM(409,814) = 332926

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FAQs on GCF of Fractions of 770/409, 1036/814

1. What is the HCF of 770,1036?

The HCF of 770,1036 is 14

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 770/409, 1036/814?

Answer: GCF of Numerators as per given numbers 770/409, 1036/814 is

GCF of Numerators i.e. for 770,1036 is 14

LCM of denominators i.e. for 409,814 is 332926.

Thus, GCF of Fractions is 14/332926.Finally, GCF of Fractions for 770/409, 1036/814 is 14/332926.