How to Find GCF of 778/978, 1781/119?

GCF of 778/978, 1781/119

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 778/978, 1781/119 i.e 1/116382 easily. The following is the detailed procedure to determine the greatest common factor of fractions 778/978, 1781/119.

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 778/978,1781/119?

Given fractions are 778/978,1781/119

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 778/978,1781/119, numerators are 778,1781

Denominators are 978,119

The GCF of 778,1781 is 1 .

LCM of 978,119 is 116382.

The greatest common factor of 778/978,1781/119 = [GCF of 778,1781]/[LCM of 978,119]= 1/116382

Therefore, the GCF of 778/978,1781/119 is 1/116382.

Greatest Common Factor of 778,1781

To find the highest common factor of 778,1781, we have to find the factors of both numbers and list the highest common factor.

The factors of 778 are 1, 2, 389, 778

The factors of 1781 are 1, 13, 137, 1781

The HCF of 778,1781 is 1.

Lets's calculate GCF of 778,1781

Greatest Common Factor (GCF) of 778,1781 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 778,1781 By Matching Biggest Common Factor Method

Now, list down the factors of 778

1,2,389,778

Now, list down the factors of 1781

1,13,137,1781

Greatest Common Factor

We found the factors 778,1781 . The biggest common factor number is the GCF number.
So the greatest common factor 778,1781 is 1.

Lets's calculate LCM of 978,119

Lowest Common Multiple of 978,119 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 116382

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/116382

Therefore, the GCF of Fractions 778/978,1781/119 is 1/116382

Least Common Multiple of 978,119 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 978,119 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(978,119) = 1

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

GCF(978,119) x common factors =1 x 1 = 1

LCM(978,119) = ( 978 × 119 ) / 1

LCM(978,119) = 116382 / 1

LCM(978,119) = 116382

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 778/978, 1781/119

1. What is the HCF of 778,1781?

The HCF of 778,1781 is 1

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 778/978, 1781/119?

Answer: GCF of Numerators as per given numbers 778/978, 1781/119 is

GCF of Numerators i.e. for 778,1781 is 1

LCM of denominators i.e. for 978,119 is 116382.

Thus, GCF of Fractions is 1/116382.Finally, GCF of Fractions for 778/978, 1781/119 is 1/116382.