How to Find GCF of 778/159, 540/643?

GCF of 778/159, 540/643

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 778/159, 540/643 i.e 2/102237 easily. The following is the detailed procedure to determine the greatest common factor of fractions 778/159, 540/643.

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 778/159,540/643?

Given fractions are 778/159,540/643

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 778/159,540/643, numerators are 778,540

Denominators are 159,643

The GCF of 778,540 is 2 .

LCM of 159,643 is 102237.

The greatest common factor of 778/159,540/643 = [GCF of 778,540]/[LCM of 159,643]= 2/102237

Therefore, the GCF of 778/159,540/643 is 2/102237.

Greatest Common Factor of 778,540

To find the highest common factor of 778,540, 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 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540

The HCF of 778,540 is 2.

Lets's calculate GCF of 778,540

Greatest Common Factor (GCF) of 778,540 By Common Division

2	778, 540
	389, 270

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

Greatest Common Factor of 778,540 By Matching Biggest Common Factor Method

Now, list down the factors of 778

1,2,389,778

Now, list down the factors of 540

1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540

Greatest Common Factor

We found the factors 778,540 . The biggest common factor number is the GCF number.
So the greatest common factor 778,540 is 2.

Lets's calculate LCM of 159,643

Lowest Common Multiple of 159,643 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 102237

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/102237

Therefore, the GCF of Fractions 778/159,540/643 is 2/102237

Least Common Multiple of 159,643 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 159,643 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(159,643) = 1

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

GCF(159,643) x common factors =1 x 1 = 1

LCM(159,643) = ( 159 × 643 ) / 1

LCM(159,643) = 102237 / 1

LCM(159,643) = 102237

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 778/159, 540/643

1. What is the HCF of 778,540?

The HCF of 778,540 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 778/159, 540/643?

Answer: GCF of Numerators as per given numbers 778/159, 540/643 is

GCF of Numerators i.e. for 778,540 is 2

LCM of denominators i.e. for 159,643 is 102237.

Thus, GCF of Fractions is 2/102237.Finally, GCF of Fractions for 778/159, 540/643 is 2/102237.