How to Find GCF of 77/218, 71/697, 234/600?

GCF of 77/218, 71/697, 234/600

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 77/218, 71/697, 234/600 i.e 1/45583800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/218, 71/697, 234/600.

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 77/218,71/697,234/600?

Given fractions are 77/218,71/697,234/600

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 77/218,71/697,234/600, numerators are 77,71,234

Denominators are 218,697,600

The GCF of 77,71,234 is 1 .

LCM of 218,697,600 is 45583800.

The greatest common factor of 77/218,71/697,234/600 = [GCF of 77,71,234]/[LCM of 218,697,600]= 1/45583800

Therefore, the GCF of 77/218,71/697,234/600 is 1/45583800.

Greatest Common Factor of 77,71,234

To find the highest common factor of 77,71,234, we have to find the factors of both numbers and list the highest common factor.

The factors of 77 are 1, 7, 11, 77

The factors of 71 are 1, 71

The factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234

The HCF of 77,71,234 is 1.

Lets's calculate GCF of 77,71,234

Greatest Common Factor (GCF) of 77,71,234 By Common Division

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

Greatest Common Factor of 77,71,234 By Matching Biggest Common Factor Method

Now, list down the factors of 77

1,7,11,77

Now, list down the factors of 71

1,71

Now, list down the factors of 234

1,2,3,6,9,13,18,26,39,78,117,234

Greatest Common Factor

We found the factors 77,71,234 . The biggest common factor number is the GCF number.
So the greatest common factor 77,71,234 is 1.

Lets's calculate LCM of 218,697,600

Lowest Common Multiple of 218,697,600 using Common Division

2	218, 697, 600
	109, 697, 300

∴ So the LCM of the given numbers is 2 x 109 x 697 x 300 = 45583800

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/45583800

Therefore, the GCF of Fractions 77/218,71/697,234/600 is 1/45583800

Least Common Multiple of 218,697,600 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 218,697,600 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(218,697,600) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(218,697,600) x common factors =1 x 2 = 2

LCM(218,697,600) = ( 218 × 697 × 600 ) / 2

LCM(218,697,600) = 91167600 / 2

LCM(218,697,600) = 45583800

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 77/218, 71/697, 234/600

1. What is the HCF of 77,71,234?

The HCF of 77,71,234 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 77/218, 71/697, 234/600?

Answer: GCF of Numerators as per given numbers 77/218, 71/697, 234/600 is

GCF of Numerators i.e. for 77,71,234 is 1

LCM of denominators i.e. for 218,697,600 is 45583800.

Thus, GCF of Fractions is 1/45583800.Finally, GCF of Fractions for 77/218, 71/697, 234/600 is 1/45583800.