How to Find GCF of 986/773, 578/619?

GCF of 986/773, 578/619

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 986/773, 578/619 i.e 34/478487 easily. The following is the detailed procedure to determine the greatest common factor of fractions 986/773, 578/619.

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 986/773,578/619?

Given fractions are 986/773,578/619

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 986/773,578/619, numerators are 986,578

Denominators are 773,619

The GCF of 986,578 is 34 .

LCM of 773,619 is 478487.

The greatest common factor of 986/773,578/619 = [GCF of 986,578]/[LCM of 773,619]= 34/478487

Therefore, the GCF of 986/773,578/619 is 34/478487.

Greatest Common Factor of 986,578

To find the highest common factor of 986,578, we have to find the factors of both numbers and list the highest common factor.

The factors of 986 are 1, 2, 17, 29, 34, 58, 493, 986

The factors of 578 are 1, 2, 17, 34, 289, 578

The HCF of 986,578 is 34.

Lets's calculate GCF of 986,578

Greatest Common Factor (GCF) of 986,578 By Common Division

2	986, 578
17	493, 289
	29, 17

∴ So the GCF of the given numbers is 2 x 17 = 34

Greatest Common Factor of 986,578 By Matching Biggest Common Factor Method

Now, list down the factors of 986

1,2,17,29,34,58,493,986

Now, list down the factors of 578

1,2,17,34,289,578

Greatest Common Factor

We found the factors 986,578 . The biggest common factor number is the GCF number.
So the greatest common factor 986,578 is 34.

Lets's calculate LCM of 773,619

Lowest Common Multiple of 773,619 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 478487

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 34/478487

Therefore, the GCF of Fractions 986/773,578/619 is 34/478487

Least Common Multiple of 773,619 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 773,619 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(773,619) = 1

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

GCF(773,619) x common factors =1 x 1 = 1

LCM(773,619) = ( 773 × 619 ) / 1

LCM(773,619) = 478487 / 1

LCM(773,619) = 478487

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FAQs on GCF of Fractions of 986/773, 578/619

1. What is the HCF of 986,578?

The HCF of 986,578 is 34

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 986/773, 578/619?

Answer: GCF of Numerators as per given numbers 986/773, 578/619 is

GCF of Numerators i.e. for 986,578 is 34

LCM of denominators i.e. for 773,619 is 478487.

Thus, GCF of Fractions is 34/478487.Finally, GCF of Fractions for 986/773, 578/619 is 34/478487.